Q1. Calculate the wavelength of light with Hz. Express it in both m and nm.

Background

Topic: Electromagnetic Radiation – Relationship between Frequency and Wavelength

This question tests your understanding of how to relate the frequency of light to its wavelength using the speed of light equation.

Key Terms and Formulas

• Frequency (): The number of cycles (waves) per second, measured in Hz (s-1).

• Wavelength (): The distance between two consecutive peaks of a wave, measured in meters (m) or nanometers (nm).

• Speed of light (): m/s

Key formula:

Step-by-Step Guidance

1. Write down the known values: Hz, m/s.

2. Rearrange the formula to solve for wavelength:

3. Plug in the values for and to calculate in meters.

4. To convert the wavelength from meters to nanometers, recall that $1= 1 \times 10^9 to get the value in nm.

Try solving on your own before revealing the answer!

Q2. What is the energy of a photon of this light (in J/photon)? A mole of photons of this light (in J/mol and kJ/mol)?

Background

Topic: Energy of Photons – Planck's Equation

This question tests your ability to calculate the energy of a single photon using its frequency, and then scale that up to a mole of photons using Avogadro's number.

Key Terms and Formulas

• Photon: A quantum of electromagnetic radiation (a particle of light).

• Planck's constant (): J·s

• Avogadro's number (): mol-1

Key formulas:

Step-by-Step Guidance

1. Write down the known values: J·s, Hz.

2. Use Planck's equation to calculate the energy of one photon:

3. Multiply the energy per photon by Avogadro's number to get the energy per mole:

4. To convert from J/mol to kJ/mol, divide your answer by $1000$.

Try solving on your own before revealing the answer!

Q3. What is a line spectrum? How would you explain to a friend who isn’t taking General Chemistry why one is so important, given the historical context described in Chapter 2? (In other words, why is hydrogen’s line spectrum such a focus of Chapter 2)?

Background

Topic: Atomic Spectra and the Bohr Model

This question is about understanding what a line spectrum is and its significance in the development of atomic theory, especially regarding hydrogen.

Key Terms and Concepts

• Line Spectrum: A spectrum showing only certain discrete wavelengths (lines) of light, rather than a continuous range.

• Bohr Model: A model of the atom that explains the discrete energy levels of electrons and the emission of specific wavelengths of light.

Step-by-Step Guidance

1. Define what a line spectrum is, contrasting it with a continuous spectrum.

2. Explain that each element has a unique line spectrum, like a fingerprint.

3. Discuss why the hydrogen line spectrum was historically important: it could not be explained by classical physics, leading to the development of quantum theory and the Bohr model.

4. Describe how the Bohr model explained the hydrogen spectrum by proposing quantized energy levels for electrons.

Try explaining this in your own words before revealing the answer!

Q4. An electron moves from the to the orbit as described in the Bohr model of the hydrogen atom. What wavelength of light is emitted?

Background

Topic: Bohr Model – Electron Transitions and Emission Spectra

This question tests your ability to use the Bohr model to calculate the wavelength of light emitted when an electron transitions between energy levels in a hydrogen atom.

Key Terms and Formulas

• Bohr Model: Describes electrons in quantized orbits around the nucleus.

• Energy Level (): The principal quantum number indicating the electron's orbit.

• Rydberg constant (): J

Key formulas:

Step-by-Step Guidance

1. Identify the initial () and final () energy levels.

2. Use the Bohr equation to calculate the energy change:

3. Plug in the values for , , and to find .

4. Relate the energy change to wavelength using , and rearrange to solve for .

5. Plug in the values for and to set up the calculation for .

Try setting up the calculation before revealing the answer!