Q: A sodium street lamp emits yellow light with a wavelength of $589\ \mathrm{nm}$. What is the frequency of this light? (Speed of light $c = 3.00 \times 10^8\ \mathrm{m/s}$)

$5.09 \times 10^{14}\ \mathrm{Hz}$

Q: What is the energy (in joules) of a single photon of ultraviolet light with a wavelength of $250\ \mathrm{nm}$? (Planck's constant $h = 6.626 \times 10^{-34}\ \mathrm{J \cdot s}$, $c = 3.00 \times 10^8\ \mathrm{m/s}$)

$7.95 \times 10^{-19}\ \mathrm{J}$

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

According to the quantum mechanical model, what does the principal quantum number $n$ primarily determine for an electron in an atom?

Accepted Answer

The energy level and size of the orbital

Question 3

A sodium street lamp emits yellow light with a wavelength of $589\ \mathrm{nm}$. What is the frequency of this light? (Speed of light $c = 3.00 	imes 10^8\ \mathrm{m/s}$)

Accepted Answer

$5.09 	imes 10^{14}\ \mathrm{Hz}$

Question 4

Which experiment provided direct evidence for the wave nature of electrons?

Accepted Answer

The double-slit experiment with electrons showing an interference pattern

Question 5

What is the energy (in joules) of a single photon of ultraviolet light with a wavelength of $250\ \mathrm{nm}$? (Planck's constant $h = 6.626 	imes 10^{-34}\ \mathrm{J \cdot s}$, $c = 3.00 	imes 10^8\ \mathrm{m/s}$)

Accepted Answer

$7.95 	imes 10^{-19}\ \mathrm{J}$

Question 6

Which statement best explains why high-energy electromagnetic radiation (such as X-rays and gamma rays) can damage biological molecules?

Accepted Answer

They have high frequencies and short wavelengths, resulting in high photon energies capable of ionizing atoms.

Question 7

According to the Heisenberg uncertainty principle, which of the following is true for an electron in an atom?

Accepted Answer

The more precisely the position is known, the less precisely the velocity is known.

Question 8

A metal surface has a threshold frequency $v_0$ for the photoelectric effect. If light of frequency $v > v_0$ is shined on the surface, what happens to the kinetic energy of the emitted electrons as the frequency of the light increases?

Accepted Answer

The kinetic energy of the electrons increases.

Question 9

Which set of quantum numbers is NOT allowed for an electron in an atom?

Accepted Answer

$n=2,\ l=2,\ m_l=0,\ m_s=+\frac{1}{2}$

Question 10

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

Accepted Answer

5

Question 11

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

Accepted Answer

Constructive interference results in a larger amplitude, while destructive interference results in cancellation or reduced amplitude.

Question 12

A hydrogen atom's electron transitions from $n=5$ to $n=2$. Which of the following statements is true?

Accepted Answer

The atom emits a photon whose energy equals the difference between the $n=5$ and $n=2$ energy levels.

Question 13

What is the de Broglie wavelength of an electron (mass $9.11 	imes 10^{-31}\ \mathrm{kg}$) moving at $2.00 	imes 10^6\ \mathrm{m/s}$? (Planck's constant $h = 6.626 	imes 10^{-34}\ \mathrm{J \cdot s}$)

Accepted Answer

$3.63 	imes 10^{-10}\ \mathrm{m}$

Question 14

Which of the following statements about atomic orbitals is correct?

Accepted Answer

A 3d orbital has a four-lobed shape.

Question 15

Which quantum number determines the number of possible orientations of an orbital in space?

Accepted Answer

Magnetic quantum number $m_l$

Question 16

If an electron in a hydrogen atom absorbs a photon and moves from $n=1$ to $n=3$, what happens to the energy of the atom?

Accepted Answer

The energy of the atom increases.

Question 17

Which of the following best explains why the emission spectrum of hydrogen consists of discrete lines?

Accepted Answer

Electrons transition between quantized energy levels, emitting photons of specific energies.

Question 18

How many orbitals are present in the $n=3$ principal energy level of an atom?

Accepted Answer

9

Question 19

Which of the following is a correct statement about the probability density function for an electron in an atom?

Accepted Answer

It represents the probability of finding the electron at a particular point in space.

Quantum Mechanics and the Atomic Model: The Strange Behavior of Electrons

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