Q: What is the relationship between the wavelength ($\lambda$) and frequency ($\nu$) of electromagnetic radiation?

$\lambda$ and $\nu$ are inversely proportional.

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

$2.64 \times 10^{20}$ photons/s

Question 1

Which of the following best describes the wave–particle duality of the electron?

Accepted Answer

Electrons exhibit both particle-like and wave-like properties depending on the experimental conditions.

Question 2

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

Accepted Answer

$5.83 	imes 10^{14}$ Hz

Question 3

Which of the following statements about the electromagnetic spectrum is correct?

Accepted Answer

Radio waves have the lowest frequency and energy.

Question 4

What is the relationship between the wavelength ($\lambda$) and frequency ($
u$) of electromagnetic radiation?

Accepted Answer

$\lambda$ and $
u$ are inversely proportional.

Question 5

Which phenomenon provides evidence for the wave nature of electrons?

Accepted Answer

Electron diffraction

Question 6

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

Accepted Answer

$2.64 	imes 10^{20}$ photons/s

Question 7

Which of the following best explains why the photoelectric effect cannot be explained by classical wave theory?

Accepted Answer

Classical theory predicts that electrons should be emitted at any frequency if the light is intense enough, but experiments show a threshold frequency is required.

Question 8

Calculate the energy of a single photon of ultraviolet light with a wavelength of $250$ nm. (Use $h = 6.626 	imes 10^{-34}$ J·s, $c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$7.95 	imes 10^{-19}$ J

Question 9

Which transition in a hydrogen atom emits light with the highest energy?

Accepted Answer

$n = 3 \rightarrow n = 2$

Question 10

According to the de Broglie relation, what happens to the wavelength of a particle as its momentum increases?

Accepted Answer

The wavelength decreases.

Question 11

Why don’t we observe wave properties for a baseball thrown at a ballpark, according to quantum mechanics?

Accepted Answer

Because the baseball’s large mass makes its de Broglie wavelength extremely small and unobservable.

Question 12

Which statement 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.

Question 13

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number ($\ell$)

Question 14

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

Accepted Answer

5

Question 15

What is the total number of orbitals in the $n = 3$ principal energy level?

Accepted Answer

9

Question 16

Which of the following transitions in a hydrogen atom would result in the emission of a photon in the visible region?

Accepted Answer

$n = 3 \rightarrow n = 2$

Question 17

How many radial nodes are present in a $3s$ orbital?

Accepted Answer

2

Question 18

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

Accepted Answer

$n$, $\ell$, $m_\ell$, and $m_s$

Question 19

Which of the following best describes the shape of a $p$ orbital?

Accepted Answer

Dumbbell-shaped

Question 20

A sodium street lamp emits yellow light with a wavelength of $589$ nm. What is the energy of a single photon of this light? ($h = 6.626 	imes 10^{-34}$ J·s, $c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$3.38 	imes 10^{-19}$ J

Quantum-Mechanical Model of the Atom: Structure, Properties, and Electron Behavior

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