Q: A green laser emits light with a wavelength of 515 nm. What is the frequency ($\nu$) of this light? ($c = 3.00 \times 10^8$ m/s)

$\nu = \dfrac{3.00 \times 10^8}{515 \times 10^{-9}} = 5.83 \times 10^{14} \text{ Hz}$

Q: Calculate the energy of a single photon with a wavelength of 337 nm. ($h = 6.626 \times 10^{-34}$ J·s, $c = 3.00 \times 10^8$ m/s)

$E = \dfrac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{337 \times 10^{-9}} = 5.90 \times 10^{-19} \text{ J}$

Q: Which quantum number determines the shape of an atomic orbital?

Angular momentum quantum number ($l$)

Q: According to the de Broglie relation, why do we not observe wave properties for macroscopic objects like baseballs?

Because their mass is so large that their de Broglie wavelength is minuscule compared to their size.

Q: Which of the following best summarizes Heisenberg’s uncertainty principle?

Either the position or the velocity of an electron can be accurately known at the same instant, but not both.

Q: Which quantum numbers are needed to uniquely describe a single electron in an atom?

Principal quantum number ($n$), angular momentum quantum number ($l$), magnetic quantum number ($m_l$), and spin quantum number ($m_s$)

Q: Which of the following statements about atomic emission spectra is correct?

Each element has a unique line spectrum because electrons transition between specific energy levels.

Q: A 100-watt light bulb emits light at a wavelength of 525 nm. How many photons are emitted per second? ($h = 6.626 \times 10^{-34}$ J·s, $c = 3.00 \times 10^8$ m/s)

First, calculate the energy per photon: $E = \dfrac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{525 \times 10^{-9}} = 3.79 \times 10^{-19}$ J. Then, $\dfrac{100}{3.79 \times 10^{-19}} = 2.64 \times 10^{20}$ photons per second.

Question 1

Which of the following best explains why electrons in atoms cannot be directly observed without altering their behavior?

Accepted Answer

Electrons are so small that any attempt to observe them, such as shining light on them, changes their energy and position.

Question 2

Which equation correctly relates the wavelength ($\lambda$) and frequency ($
u$) of electromagnetic radiation, given the speed of light ($c$)?

Accepted Answer

$c = \lambda 
u$

Question 3

A green laser emits light with a wavelength of 515 nm. What is the frequency ($
u$) of this light? ($c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$
u = \dfrac{3.00 	imes 10^8}{515 	imes 10^{-9}} = 5.83 	imes 10^{14} 	ext{ Hz}$

Question 4

Which of the following statements about the photoelectric effect is correct?

Accepted Answer

Electrons are only ejected from a metal surface if the incident light has a frequency above a certain threshold, regardless of intensity.

Question 5

Calculate the energy of a single photon with a wavelength of 337 nm. ($h = 6.626 	imes 10^{-34}$ J·s, $c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$E = \dfrac{6.626 	imes 10^{-34} 	imes 3.00 	imes 10^8}{337 	imes 10^{-9}} = 5.90 	imes 10^{-19} 	ext{ J}$

Question 6

Arrange the following types of electromagnetic radiation in order of increasing energy per photon: visible, X-ray, infrared.

Accepted Answer

infrared < visible < X-ray

Question 7

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number ($l$)

Question 8

How many orbitals are present in the $n = 4$ principal energy level?

Accepted Answer

16

Question 9

Which transition in a hydrogen atom emits light with the shortest wavelength?

Accepted Answer

$n = 3 \rightarrow n = 2$

Question 10

According to the de Broglie relation, why do we not observe wave properties for macroscopic objects like baseballs?

Accepted Answer

Because their mass is so large that their de Broglie wavelength is minuscule compared to their size.

Question 11

Which of the following best summarizes Heisenberg’s uncertainty principle?

Accepted Answer

Either the position or the velocity of an electron can be accurately known at the same instant, but not both.

Question 12

Which quantum numbers are needed to uniquely describe a single electron in an atom?

Accepted Answer

Principal quantum number ($n$), angular momentum quantum number ($l$), magnetic quantum number ($m_l$), and spin quantum number ($m_s$)

Question 13

Which of the following statements about atomic emission spectra is correct?

Accepted Answer

Each element has a unique line spectrum because electrons transition between specific energy levels.

Question 14

What is the total number of $d$ orbitals in the $n = 5$ shell?

Accepted Answer

5

Question 15

Which property of light determines its color?

Accepted Answer

Wavelength

Question 16

A 100-watt light bulb emits light at a wavelength of 525 nm. How many photons are emitted per second? ($h = 6.626 	imes 10^{-34}$ J·s, $c = 3.00 	imes 10^8$ m/s)

Accepted Answer

First, calculate the energy per photon: $E = \dfrac{6.626 	imes 10^{-34} 	imes 3.00 	imes 10^8}{525 	imes 10^{-9}} = 3.79 	imes 10^{-19}$ J. Then, $\dfrac{100}{3.79 	imes 10^{-19}} = 2.64 	imes 10^{20}$ photons per second.

Question 17

Which of the following best describes the difference between constructive and destructive interference?

Accepted Answer

Constructive interference occurs when waves are in phase and add together; destructive interference occurs when waves are out of phase and cancel each other.

Question 18

Which quantum number(s) determine the orientation of an orbital in space?

Accepted Answer

Magnetic quantum number ($m_l$)

Quantum-Mechanical Model of the Atom: Structure, Light, and Atomic Spectra

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