{"type":"doc","content":[{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q1a. What is the frequency of light having a wavelength of 456 nm?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Relationship between wavelength and frequency of light"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your understanding of how the speed of light relates to wavelength and frequency."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key formula:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"c = \\lambda \\nu"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"c"}},{"type":"text","text":" = speed of light ("},{"type":"inlineMath","attrs":{"latex":"3.00 \\times 10^8"}},{"type":"text","text":" m/s)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda"}},{"type":"text","text":" = wavelength (in meters)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\nu"}},{"type":"text","text":" = frequency (in Hz)"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Convert the wavelength from nanometers to meters: "},{"type":"inlineMath","attrs":{"latex":"\\lambda = 456 \\text{ nm} = 456 \\times 10^{-9} \\text{ m}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use the formula "},{"type":"inlineMath","attrs":{"latex":"c = \\lambda \\nu"}},{"type":"text","text":" and rearrange to solve for frequency: "},{"type":"inlineMath","attrs":{"latex":"\\nu = \\frac{c}{\\lambda}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Plug in the values for "},{"type":"inlineMath","attrs":{"latex":"c"}},{"type":"text","text":" and "},{"type":"inlineMath","attrs":{"latex":"\\lambda"}},{"type":"text","text":" to set up the calculation."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"6.58 \\times 10^{14}"}},{"type":"text","marks":[{"type":"bold"}],"text":" Hz"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\nu = \\frac{3.00 \\times 10^8}{456 \\times 10^{-9}} = 6.58 \\times 10^{14}"}},{"type":"text","text":" Hz$"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This is the frequency of light with a wavelength of 456 nm."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q1b. What is the wavelength (in nm) of radiation having a frequency of "},{"type":"inlineMath","attrs":{"latex":"2.45 \\times 10^9"}},{"type":"text","marks":[{"type":"bold"}],"text":" Hz?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Relationship between wavelength and frequency"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to convert frequency to wavelength using the speed of light."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key formula:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"c = \\lambda \\nu"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"c"}},{"type":"text","text":" = speed of light ("},{"type":"inlineMath","attrs":{"latex":"3.00 \\times 10^8"}},{"type":"text","text":" m/s)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda"}},{"type":"text","text":" = wavelength (in meters)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\nu"}},{"type":"text","text":" = frequency (in Hz)"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Rearrange the formula to solve for wavelength: "},{"type":"inlineMath","attrs":{"latex":"\\lambda = \\frac{c}{\\nu}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Plug in the values for "},{"type":"inlineMath","attrs":{"latex":"c"}},{"type":"text","text":" and "},{"type":"inlineMath","attrs":{"latex":"\\nu"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the wavelength in meters, then convert to nanometers ("},{"type":"inlineMath","attrs":{"latex":"1 \\text{ m} = 10^9 \\text{ nm}"}},{"type":"text","text":")."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: $122"},{"type":"inlineMath","attrs":{"latex":" mm ($1.22 \\times 10^8"}},{"type":"text","marks":[{"type":"bold"}],"text":" nm)"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda = \\frac{3.00 \\times 10^8}{2.45 \\times 10^9} = 0.122"}},{"type":"text","text":" m$"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Converted to nanometers: "},{"type":"inlineMath","attrs":{"latex":"0.122 \\text{ m} \\times 10^9 = 1.22 \\times 10^8"}},{"type":"text","text":" nm."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q1c. Calculate the energy (in joules) of a single photon associated with a frequency of "},{"type":"inlineMath","attrs":{"latex":"7.5 \\times 10^{14}"}},{"type":"text","marks":[{"type":"bold"}],"text":" Hz."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Photon energy and frequency"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to use Planck's equation to find the energy of a photon."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key formula:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E"}},{"type":"text","text":" = energy (in joules)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"h"}},{"type":"text","text":" = Planck's constant ("},{"type":"inlineMath","attrs":{"latex":"6.63 \\times 10^{-34}"}},{"type":"text","text":" J·s)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\nu"}},{"type":"text","text":" = frequency (in Hz)"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Write down the formula: "},{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Plug in the values for "},{"type":"inlineMath","attrs":{"latex":"h"}},{"type":"text","text":" and "},{"type":"inlineMath","attrs":{"latex":"\\nu"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the multiplication to find the energy in joules."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"4.97 \\times 10^{-19}"}},{"type":"text","marks":[{"type":"bold"}],"text":" J"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E = (6.63 \\times 10^{-34}) \\times (7.5 \\times 10^{14}) = 4.97 \\times 10^{-19}"}},{"type":"text","text":" J$"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This is the energy of a single photon with the given frequency."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q2. Calculate the wavelength, in meters, of microwave radiation that corresponds to an energy of 2.63 J/mol of photons."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Energy per photon and wavelength"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to relate energy per mole to energy per photon, and then to wavelength."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key formulas:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"c = \\lambda \\nu"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E"}},{"type":"text","text":" = energy per photon (in joules)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"h"}},{"type":"text","text":" = Planck's constant ("},{"type":"inlineMath","attrs":{"latex":"6.63 \\times 10^{-34}"}},{"type":"text","text":" J·s)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\nu"}},{"type":"text","text":" = frequency (in Hz)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"c"}},{"type":"text","text":" = speed of light ("},{"type":"inlineMath","attrs":{"latex":"3.00 \\times 10^8"}},{"type":"text","text":" m/s)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda"}},{"type":"text","text":" = wavelength (in meters)"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Convert the energy from J/mol to J/photon using Avogadro's number ("},{"type":"inlineMath","attrs":{"latex":"6.022 \\times 10^{23}"}},{"type":"text","text":" mol"},{"type":"inlineMath","attrs":{"latex":"^{-1}"}},{"type":"text","text":")."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use "},{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}},{"type":"text","text":" to solve for frequency: "},{"type":"inlineMath","attrs":{"latex":"\\nu = \\frac{E}{h}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use "},{"type":"inlineMath","attrs":{"latex":"c = \\lambda \\nu"}},{"type":"text","text":" to solve for wavelength: "},{"type":"inlineMath","attrs":{"latex":"\\lambda = \\frac{c}{\\nu}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the calculation for "},{"type":"inlineMath","attrs":{"latex":"\\lambda"}},{"type":"text","text":" in meters."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"4.54 \\times 10^{-2}"}},{"type":"text","marks":[{"type":"bold"}],"text":" m"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"After converting energy per photon and using the formulas, the wavelength is "},{"type":"inlineMath","attrs":{"latex":"4.54 \\times 10^{-2}"}},{"type":"text","text":" meters."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q3. Light of wavelength 221.0 nm striking a sample of tungsten causes electrons to be ejected with a speed of "},{"type":"inlineMath","attrs":{"latex":"6.04 \\times 10^5"}},{"type":"text","marks":[{"type":"bold"}],"text":" m/s. Calculate the work function (W) / binding energy of tungsten."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Photoelectric effect"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your understanding of the photoelectric effect and how to calculate the work function using photon energy and kinetic energy."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key formulas:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E = W + KE"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"KE = \\frac{1}{2} m v^2"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E"}},{"type":"text","text":" = energy of photon (in joules)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"W"}},{"type":"text","text":" = work function (in joules)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"KE"}},{"type":"text","text":" = kinetic energy of ejected electron (in joules)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"m"}},{"type":"text","text":" = mass of electron ("},{"type":"inlineMath","attrs":{"latex":"9.10939 \\times 10^{-28}"}},{"type":"text","text":" g, convert to kg)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"v"}},{"type":"text","text":" = speed of electron (in m/s)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"h"}},{"type":"text","text":" = Planck's constant ("},{"type":"inlineMath","attrs":{"latex":"6.63 \\times 10^{-34}"}},{"type":"text","text":" J·s)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\nu"}},{"type":"text","text":" = frequency (in Hz)"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Convert the wavelength from nm to meters: "},{"type":"inlineMath","attrs":{"latex":"221.0 \\text{ nm} = 221.0 \\times 10^{-9} \\text{ m}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the frequency using "},{"type":"inlineMath","attrs":{"latex":"\\nu = \\frac{c}{\\lambda}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the energy of the photon: "},{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the kinetic energy of the electron: "},{"type":"inlineMath","attrs":{"latex":"KE = \\frac{1}{2} m v^2"}},{"type":"text","text":" (convert mass to kg)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the equation "},{"type":"inlineMath","attrs":{"latex":"W = E - KE"}},{"type":"text","text":" to solve for the work function."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"6.13 \\times 10^{-19}"}},{"type":"text","marks":[{"type":"bold"}],"text":" J"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The work function is calculated by subtracting the kinetic energy from the photon energy."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q4. The work function of a given metal is "},{"type":"inlineMath","attrs":{"latex":"1.66 \\times 10^{-17}"}},{"type":"text","marks":[{"type":"bold"}],"text":" J. If the wavelength of the radiation incident on the metal is "},{"type":"inlineMath","attrs":{"latex":"8.8 \\times 10^{-9}"}},{"type":"text","marks":[{"type":"bold"}],"text":" m, what is the kinetic energy of the ejected electron?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Photoelectric effect"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to calculate the kinetic energy of an ejected electron given the work function and wavelength of incident light."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key formulas:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E = W + KE"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\nu = \\frac{c}{\\lambda}"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E"}},{"type":"text","text":" = energy of photon (in joules)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"W"}},{"type":"text","text":" = work function (in joules)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"KE"}},{"type":"text","text":" = kinetic energy (in joules)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"h"}},{"type":"text","text":" = Planck's constant ("},{"type":"inlineMath","attrs":{"latex":"6.63 \\times 10^{-34}"}},{"type":"text","text":" J·s)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"c"}},{"type":"text","text":" = speed of light ("},{"type":"inlineMath","attrs":{"latex":"3.00 \\times 10^8"}},{"type":"text","text":" m/s)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda"}},{"type":"text","text":" = wavelength (in meters)"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the frequency: "},{"type":"inlineMath","attrs":{"latex":"\\nu = \\frac{c}{\\lambda}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the energy of the photon: "},{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the equation "},{"type":"inlineMath","attrs":{"latex":"KE = E - W"}},{"type":"text","text":" to solve for kinetic energy."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"1.60 \\times 10^{-17}"}},{"type":"text","marks":[{"type":"bold"}],"text":" J"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The kinetic energy is found by subtracting the work function from the photon energy."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q5. Calculate the wavelength (nm) of light that strikes a metal with a threshold frequency of "},{"type":"inlineMath","attrs":{"latex":"2.84 \\times 10^{14}"}},{"type":"text","marks":[{"type":"bold"}],"text":" s"},{"type":"inlineMath","attrs":{"latex":"^{-1}"}},{"type":"text","marks":[{"type":"bold"}],"text":" and ejects an electron with a kinetic energy of "},{"type":"inlineMath","attrs":{"latex":"5.48 \\times 10^{-19}"}},{"type":"text","marks":[{"type":"bold"}],"text":" J."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Photoelectric effect and threshold frequency"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to relate threshold frequency, kinetic energy, and wavelength of incident light."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key formulas:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E = h \\nu_{th} + KE"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda = \\frac{c}{\\nu}"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E"}},{"type":"text","text":" = energy of photon (in joules)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"h"}},{"type":"text","text":" = Planck's constant ("},{"type":"inlineMath","attrs":{"latex":"6.63 \\times 10^{-34}"}},{"type":"text","text":" J·s)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\nu_{th}"}},{"type":"text","text":" = threshold frequency (in Hz)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"KE"}},{"type":"text","text":" = kinetic energy (in joules)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda"}},{"type":"text","text":" = wavelength (in meters or nm)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"c"}},{"type":"text","text":" = speed of light ("},{"type":"inlineMath","attrs":{"latex":"3.00 \\times 10^8"}},{"type":"text","text":" m/s)"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the total energy of the photon: "},{"type":"inlineMath","attrs":{"latex":"E = h \\nu_{th} + KE"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use "},{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}},{"type":"text","text":" to solve for the frequency of the incident light."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the wavelength: "},{"type":"inlineMath","attrs":{"latex":"\\lambda = \\frac{c}{\\nu}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Convert the wavelength to nanometers."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: $312$ nm"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The wavelength of the incident light is $312$ nm."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q6. Use the Bohr equation to find the wavelength (in nm) of the photon emitted when an H atom undergoes a transition from n=5 to n=2."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Bohr model and electronic transitions"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to use the Bohr equation to calculate the wavelength of emitted photons during electronic transitions in hydrogen."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key formulas:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\Delta E = -2.18 \\times 10^{-18} \\left( \\frac{1}{n_f^2} - \\frac{1}{n_i^2} \\right)"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda = \\frac{c}{\\nu}"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"n_i"}},{"type":"text","text":" = initial energy level (5)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"n_f"}},{"type":"text","text":" = final energy level (2)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\Delta E"}},{"type":"text","text":" = energy difference (in joules)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"h"}},{"type":"text","text":" = Planck's constant"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"c"}},{"type":"text","text":" = speed of light"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda"}},{"type":"text","text":" = wavelength (in meters or nm)"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate "},{"type":"inlineMath","attrs":{"latex":"\\Delta E"}},{"type":"text","text":" using the Bohr equation for "},{"type":"inlineMath","attrs":{"latex":"n_i = 5"}},{"type":"text","text":" and "},{"type":"inlineMath","attrs":{"latex":"n_f = 2"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use "},{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}},{"type":"text","text":" to solve for frequency."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use "},{"type":"inlineMath","attrs":{"latex":"\\lambda = \\frac{c}{\\nu}"}},{"type":"text","text":" to solve for wavelength."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Convert the wavelength to nanometers."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: $434$ nm"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The wavelength of the photon emitted is $434$ nm."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q7. How many lines would be in the emission spectrum of hydrogen if the hydrogen atom had only 10 energy levels?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Emission spectra and energy levels"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your understanding of how many possible transitions (lines) can occur between energy levels."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key concept:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The number of spectral lines is given by the formula:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\text{Number of lines} = \\frac{n(n-1)}{2}"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"n"}},{"type":"text","text":" = number of energy levels"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify the number of energy levels: "},{"type":"inlineMath","attrs":{"latex":"n = 10"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use the formula "},{"type":"inlineMath","attrs":{"latex":"\\frac{n(n-1)}{2}"}},{"type":"text","text":" to set up the calculation."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: 45 lines"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"With 10 energy levels, there are "},{"type":"inlineMath","attrs":{"latex":"\\frac{10 \\times 9}{2} = 45"}},{"type":"text","text":" possible emission lines."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q8. An electron in the hydrogen atom in an excited state with n = 7 drops to a lower energy level and emits a photon of wavelength 1006 nm. What is the final energy level of the electron?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Bohr model and electronic transitions"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to use the Bohr equation and photon wavelength to determine the final energy level after a transition."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key formulas:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\Delta E = -2.18 \\times 10^{-18} \\left( \\frac{1}{n_f^2} - \\frac{1}{n_i^2} \\right)"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda = \\frac{c}{\\nu}"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"n_i"}},{"type":"text","text":" = initial energy level (7)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"n_f"}},{"type":"text","text":" = final energy level (unknown)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda"}},{"type":"text","text":" = wavelength (1006 nm)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"h"}},{"type":"text","text":" = Planck's constant"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"c"}},{"type":"text","text":" = speed of light"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Convert the wavelength to meters: "},{"type":"inlineMath","attrs":{"latex":"1006 \\text{ nm} = 1006 \\times 10^{-9} \\text{ m}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the frequency: "},{"type":"inlineMath","attrs":{"latex":"\\nu = \\frac{c}{\\lambda}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the energy of the photon: "},{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the Bohr equation and solve for "},{"type":"inlineMath","attrs":{"latex":"n_f"}},{"type":"text","text":" using the calculated energy and "},{"type":"inlineMath","attrs":{"latex":"n_i = 7"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"n_f = 3"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The final energy level is "},{"type":"inlineMath","attrs":{"latex":"n = 3"}},{"type":"text","text":"."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q9a. What is the wavelength of the photon needed for an electron to make a transition from E1 to E4?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Energy transitions and photon wavelength"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to calculate the energy difference and corresponding photon wavelength for a transition between energy levels."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key formulas:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\Delta E = E_4 - E_1"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda = \\frac{c}{\\nu}"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E_1"}},{"type":"text","text":" = "},{"type":"inlineMath","attrs":{"latex":"-1.5 \\times 10^{-18}"}},{"type":"text","text":" J"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E_4"}},{"type":"text","text":" = "},{"type":"inlineMath","attrs":{"latex":"-1.0 \\times 10^{-19}"}},{"type":"text","text":" J"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\Delta E"}},{"type":"text","text":" = energy difference"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"h"}},{"type":"text","text":" = Planck's constant"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"c"}},{"type":"text","text":" = speed of light"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the energy difference: "},{"type":"inlineMath","attrs":{"latex":"\\Delta E = E_4 - E_1"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use "},{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}},{"type":"text","text":" to solve for frequency."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use "},{"type":"inlineMath","attrs":{"latex":"\\lambda = \\frac{c}{\\nu}"}},{"type":"text","text":" to solve for wavelength."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"1.35 \\times 10^{-7}"}},{"type":"text","marks":[{"type":"bold"}],"text":" m"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The wavelength needed for the transition is "},{"type":"inlineMath","attrs":{"latex":"1.35 \\times 10^{-7}"}},{"type":"text","text":" meters."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q9b. What is the energy (in joules) a photon must have to excite an electron from E2 to E3?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Energy transitions"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to calculate the energy required for a transition between two energy levels."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key formula:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\Delta E = E_3 - E_2"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E_2"}},{"type":"text","text":" = "},{"type":"inlineMath","attrs":{"latex":"-1.0 \\times 10^{-18}"}},{"type":"text","text":" J"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E_3"}},{"type":"text","text":" = "},{"type":"inlineMath","attrs":{"latex":"-5.0 \\times 10^{-19}"}},{"type":"text","text":" J"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the energy difference: "},{"type":"inlineMath","attrs":{"latex":"\\Delta E = E_3 - E_2"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"5.0 \\times 10^{-19}"}},{"type":"text","marks":[{"type":"bold"}],"text":" J"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The photon must have an energy of "},{"type":"inlineMath","attrs":{"latex":"5.0 \\times 10^{-19}"}},{"type":"text","text":" J."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q9c. When an electron drops from the E3 level to the E1 level, the atom is said to undergo emission. Calculate the wavelength of the photon emitted in this process."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Emission and photon wavelength"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to calculate the wavelength of a photon emitted during an energy level transition."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key formulas:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\Delta E = E_1 - E_3"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda = \\frac{c}{\\nu}"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E_1"}},{"type":"text","text":" = "},{"type":"inlineMath","attrs":{"latex":"-1.5 \\times 10^{-18}"}},{"type":"text","text":" J"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E_3"}},{"type":"text","text":" = "},{"type":"inlineMath","attrs":{"latex":"-5.0 \\times 10^{-19}"}},{"type":"text","text":" J"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the energy difference: "},{"type":"inlineMath","attrs":{"latex":"\\Delta E = E_1 - E_3"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use "},{"type":"inlineMath","attrs":{"latex":"E = h \\nu"}},{"type":"text","text":" to solve for frequency."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use "},{"type":"inlineMath","attrs":{"latex":"\\lambda = \\frac{c}{\\nu}"}},{"type":"text","text":" to solve for wavelength."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"8.87 \\times 10^{-8}"}},{"type":"text","marks":[{"type":"bold"}],"text":" m"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The wavelength of the emitted photon is "},{"type":"inlineMath","attrs":{"latex":"8.87 \\times 10^{-8}"}},{"type":"text","text":" meters."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q10. Estimate the wavelength (in nm) of a proton moving at "},{"type":"inlineMath","attrs":{"latex":"2.90 \\times 10^8"}},{"type":"text","marks":[{"type":"bold"}],"text":" m/s (mass of a proton = "},{"type":"inlineMath","attrs":{"latex":"1.673 \\times 10^{-24}"}},{"type":"text","marks":[{"type":"bold"}],"text":" g)."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: de Broglie wavelength"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to calculate the wavelength of a moving particle using the de Broglie equation."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key formula:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda = \\frac{h}{mv}"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\lambda"}},{"type":"text","text":" = wavelength (in meters or nm)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"h"}},{"type":"text","text":" = Planck's constant ("},{"type":"inlineMath","attrs":{"latex":"6.63 \\times 10^{-34}"}},{"type":"text","text":" J·s)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"m"}},{"type":"text","text":" = mass of proton (convert to kg)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"v"}},{"type":"text","text":" = velocity (in m/s)"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Convert the mass from grams to kilograms."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Plug the values into the de Broglie equation: "},{"type":"inlineMath","attrs":{"latex":"\\lambda = \\frac{h}{mv}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the wavelength in meters, then convert to nanometers."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: "},{"type":"inlineMath","attrs":{"latex":"1.36 \\times 10^{-6}"}},{"type":"text","marks":[{"type":"bold"}],"text":" nm"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The wavelength is "},{"type":"inlineMath","attrs":{"latex":"1.36 \\times 10^{-6}"}},{"type":"text","text":" nanometers."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q11a. The mass of a baseball is 142 g. Calculate the uncertainty in position if the velocity is 100.0 mi/h ± 1.0%. ("},{"type":"inlineMath","attrs":{"latex":"1 \\text{ mi} = 1609 \\text{ m}"}},{"type":"text","marks":[{"type":"bold"}],"text":"). 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The mass of an electron is "},{"type":"inlineMath","attrs":{"latex":"9.10939 \\times 10^{-31}"}},{"type":"text","marks":[{"type":"bold"}],"text":" kg. Calculate the uncertainty in position if the velocity is 100.0 mi/h ± 1.0%. 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What is the maximum number of electrons that could be designated by the quantum numbers n = 3, ℓ = 2?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Quantum numbers and electron configuration"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your understanding of how quantum numbers determine electron capacity in subshells."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key concept:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For a given "},{"type":"inlineMath","attrs":{"latex":"n"}},{"type":"text","text":" and "},{"type":"inlineMath","attrs":{"latex":"\\ell"}},{"type":"text","text":", the maximum number of electrons is "},{"type":"inlineMath","attrs":{"latex":"2(2\\ell + 1)"}},{"type":"text","text":"."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Where:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"n"}},{"type":"text","text":" = principal quantum number"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\ell"}},{"type":"text","text":" = angular momentum quantum number"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For "},{"type":"inlineMath","attrs":{"latex":"\\ell = 2"}},{"type":"text","text":", calculate the number of orbitals: "},{"type":"inlineMath","attrs":{"latex":"2\\ell + 1"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Multiply by 2 for the maximum number of electrons (spin up and spin down)."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer: