Q: A hydrogen atom's electron transitions from $n_i = 3$ to $n_f = 2$. Using the Bohr model equation $\Delta E = -2.18 \times 10^{-18} \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)$, what is the energy (in joules) released during this transition?

$\Delta E = -2.18 \times 10^{-18} \left( \frac{1}{2^2} - \frac{1}{3^2} \right) = -2.18 \times 10^{-18} \left( \frac{1}{4} - \frac{1}{9} \right) = -2.18 \times 10^{-18} \left( 0.25 - 0.111 \right) = -2.18 \times 10^{-18} \times 0.139 = -3.03 \times 10^{-19} \text{ J}$

Q: If you have 12.0 g of carbon, how many moles of carbon atoms do you have? (Atomic mass of carbon = 12.0 g/mol)

$\text{Moles} = \frac{12.0\ \text{g}}{12.0\ \text{g/mol}} = 1.0\ \text{mol}$

Q: A sample contains two isotopes of chlorine: $^{35}\text{Cl}$ (75.8% abundance, mass = 34.97 amu) and $^{37}\text{Cl}$ (24.2% abundance, mass = 36.97 amu). What is the weighted average atomic mass?

$\text{Average mass} = (0.758 \times 34.97) + (0.242 \times 36.97) = 26.52 + 8.95 = 35.47\ \text{amu}$

Q: What is the energy of a photon with a wavelength of $500\ \text{nm}$? ($h = 6.626 \times 10^{-34}\ \text{J}\cdot\text{s}$, $c = 3.00 \times 10^8\ \text{m/s}$)

$E = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{500 \times 10^{-9}} = 3.98 \times 10^{-19}\ \text{J}$

Q: According to the Heisenberg uncertainty principle, which of the following statements is correct?

$\Delta x \times m \Delta v > \frac{h}{4\pi}$

Q: If a photon with energy $5.0 \times 10^{-19}\ \text{J}$ strikes a metal with a binding energy of $4.0 \times 10^{-19}\ \text{J}$, what is the kinetic energy of the ejected electron?

$\text{KE} = E_{\text{photon}} - E_{\text{binding}} = 5.0 \times 10^{-19} - 4.0 \times 10^{-19} = 1.0 \times 10^{-19}\ \text{J}$

Q: A student measures the mass of a sample as 4.50 g and the volume as 1.2 mL. What is the density, reported with the correct number of significant figures?

$\text{Density} = \frac{4.50\ \text{g}}{1.2\ \text{mL}} = 3.8\ \text{g/mL}$

Q: How many atoms are in 2.00 g of magnesium? (Atomic mass of Mg = 24.3 g/mol, Avogadro's number $= 6.02 \times 10^{23}$)

$\text{Moles Mg} = \frac{2.00}{24.3} = 0.0823\ \text{mol}$; $\text{Atoms} = 0.0823 \times 6.02 \times 10^{23} = 4.95 \times 10^{22}$

Question 1

A hydrogen atom's electron transitions from $n_i = 3$ to $n_f = 2$. Using the Bohr model equation $\Delta E = -2.18 	imes 10^{-18} \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} ight)$, what is the energy (in joules) released during this transition?

Accepted Answer

$\Delta E = -2.18 	imes 10^{-18} \left( \frac{1}{2^2} - \frac{1}{3^2} ight) = -2.18 	imes 10^{-18} \left( \frac{1}{4} - \frac{1}{9} ight) = -2.18 	imes 10^{-18} \left( 0.25 - 0.111 ight) = -2.18 	imes 10^{-18} 	imes 0.139 = -3.03 	imes 10^{-19} 	ext{ J}$

Question 2

Which law states that the ratio of the masses of elements in a compound is always the same, regardless of the sample size?

Accepted Answer

Law of Definite Proportions

Question 3

If you have 12.0 g of carbon, how many moles of carbon atoms do you have? (Atomic mass of carbon = 12.0 g/mol)

Accepted Answer

$	ext{Moles} = \frac{12.0\ 	ext{g}}{12.0\ 	ext{g/mol}} = 1.0\ 	ext{mol}$

Question 4

Which equation is used to calculate the wavelength of a particle according to De Broglie?

Accepted Answer

$\lambda = \frac{h}{mv}$

Question 5

A sample contains two isotopes of chlorine: $^{35}	ext{Cl}$ (75.8% abundance, mass = 34.97 amu) and $^{37}	ext{Cl}$ (24.2% abundance, mass = 36.97 amu). What is the weighted average atomic mass?

Accepted Answer

$	ext{Average mass} = (0.758 	imes 34.97) + (0.242 	imes 36.97) = 26.52 + 8.95 = 35.47\ 	ext{amu}$

Question 6

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number ($l$)

Question 7

What is the energy of a photon with a wavelength of $500\ 	ext{nm}$? ($h = 6.626 	imes 10^{-34}\ 	ext{J}\cdot	ext{s}$, $c = 3.00 	imes 10^8\ 	ext{m/s}$)

Accepted Answer

$E = \frac{hc}{\lambda} = \frac{6.626 	imes 10^{-34} 	imes 3.00 	imes 10^8}{500 	imes 10^{-9}} = 3.98 	imes 10^{-19}\ 	ext{J}$

Question 8

According to the Heisenberg uncertainty principle, which of the following statements is correct?

Accepted Answer

$\Delta x 	imes m \Delta v > \frac{h}{4\pi}$

Question 9

If a photon with energy $5.0 	imes 10^{-19}\ 	ext{J}$ strikes a metal with a binding energy of $4.0 	imes 10^{-19}\ 	ext{J}$, what is the kinetic energy of the ejected electron?

Accepted Answer

$	ext{KE} = E_{	ext{photon}} - E_{	ext{binding}} = 5.0 	imes 10^{-19} - 4.0 	imes 10^{-19} = 1.0 	imes 10^{-19}\ 	ext{J}$

Question 10

Which of the following is NOT a criterion that defines a wave?

Accepted Answer

Density

Question 11

A student measures the mass of a sample as 4.50 g and the volume as 1.2 mL. What is the density, reported with the correct number of significant figures?

Accepted Answer

$	ext{Density} = \frac{4.50\ 	ext{g}}{1.2\ 	ext{mL}} = 3.8\ 	ext{g/mL}$

Question 12

How many atoms are in 2.00 g of magnesium? (Atomic mass of Mg = 24.3 g/mol, Avogadro's number $= 6.02 	imes 10^{23}$)

Accepted Answer

$	ext{Moles Mg} = \frac{2.00}{24.3} = 0.0823\ 	ext{mol}$; $	ext{Atoms} = 0.0823 	imes 6.02 	imes 10^{23} = 4.95 	imes 10^{22}$

Question 13

Which quantum number(s) determine the energy of an electron in a multi-electron atom?

Accepted Answer

Principal quantum number ($n$) and angular momentum quantum number ($l$)

Question 14

If $n = 3$, what are the possible values for $l$?

Accepted Answer

$l = 0, 1, 2$

Question 15

A compound contains 8.0 g of oxygen and 1.0 g of hydrogen. If another sample contains 16.0 g of oxygen, how many grams of hydrogen must it contain to obey the law of definite proportions?

Accepted Answer

$	ext{Ratio} = \frac{8.0}{1.0} = 8.0$; $	ext{Hydrogen} = \frac{16.0}{8.0} = 2.0\ 	ext{g}$

Question 16

Which conversion factor would you use to convert from moles of a substance to number of atoms?

Accepted Answer

$6.02 	imes 10^{23}\ 	ext{atoms/mol}$

Question 17

A student needs to convert 5.0 km to cm. Which sequence of conversion factors should be used?

Accepted Answer

$5.0\ 	ext{km} 	imes \frac{1000\ 	ext{m}}{1\ 	ext{km}} 	imes \frac{100\ 	ext{cm}}{1\ 	ext{m}}$

Question 18

Which statement best describes the law of conservation of mass?

Accepted Answer

The total mass of reactants equals the total mass of products in a chemical reaction.

Essential General Chemistry Exam 1 Study Guide: Atoms, Quantum Mechanics, and Measurement

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