Q: A mercury streetlamp emits light with a wavelength of $436\ \mathrm{nm}$. What is the frequency of this light? (Speed of light $c = 3.00 \times 10^8\ \mathrm{m/s}$)

$6.88 \times 10^{14}\ \mathrm{Hz}$

Q: A photon of ultraviolet light has a wavelength of $250\ \mathrm{nm}$. What is the energy of one mole of these photons? ($h = 6.626 \times 10^{-34}\ \mathrm{J\cdot s}$, $c = 3.00 \times 10^8\ \mathrm{m/s}$, $N_A = 6.022 \times 10^{23}\ \mathrm{mol}^{-1}$)

$4.78 \times 10^5\ \mathrm{J/mol}$

Q: A medical X-ray has a frequency of $9.55 \times 10^{17}\ \mathrm{Hz}$. What is its wavelength in meters? ($c = 3.00 \times 10^8\ \mathrm{m/s}$)

$3.14 \times 10^{-10}\ \mathrm{m}$

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

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

Question 1

Which of the following statements best explains why X-rays can be used to image bones inside the human body, while visible light cannot?

Accepted Answer

X-rays have a much shorter wavelength and higher energy than visible light, allowing them to penetrate soft tissue but be absorbed by denser materials like bone.

Question 2

A mercury streetlamp emits light with a wavelength of $436\ \mathrm{nm}$. What is the frequency of this light? (Speed of light $c = 3.00 	imes 10^8\ \mathrm{m/s}$)

Accepted Answer

$6.88 	imes 10^{14}\ \mathrm{Hz}$

Question 3

Which phenomenon provides direct evidence for the wave nature of light?

Accepted Answer

The formation of an interference pattern in a double-slit experiment.

Question 4

A photon of ultraviolet light has a wavelength of $250\ \mathrm{nm}$. What is the energy of one mole of these photons? ($h = 6.626 	imes 10^{-34}\ \mathrm{J\cdot s}$, $c = 3.00 	imes 10^8\ \mathrm{m/s}$, $N_A = 6.022 	imes 10^{23}\ \mathrm{mol}^{-1}$)

Accepted Answer

$4.78 	imes 10^5\ \mathrm{J/mol}$

Question 5

Which of the following best describes the photoelectric effect?

Accepted Answer

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

Question 6

According to the Bohr model, what happens when an electron in a hydrogen atom transitions from $n=4$ to $n=2$?

Accepted Answer

A photon is emitted with energy equal to the difference between the $n=4$ and $n=2$ energy levels.

Question 7

Which of the following sets of quantum numbers is NOT allowed for an electron in an atom?

Accepted Answer

$n=2,\ l=1,\ m_l=2$

Question 8

A medical X-ray has a frequency of $9.55 	imes 10^{17}\ \mathrm{Hz}$. What is its wavelength in meters? ($c = 3.00 	imes 10^8\ \mathrm{m/s}$)

Accepted Answer

$3.14 	imes 10^{-10}\ \mathrm{m}$

Question 9

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number $l$

Question 10

How many orbitals are present in the $n=4$ shell of an atom?

Accepted Answer

$16$

Question 11

Which of the following best describes the Heisenberg Uncertainty Principle?

Accepted Answer

It is impossible to simultaneously know both the exact position and exact momentum of an electron.

Question 12

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

Accepted Answer

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

Question 13

Which of the following transitions in a hydrogen atom would emit a photon with the highest energy?

Accepted Answer

From $n=2$ to $n=1$

Question 14

Which statement about atomic orbitals is correct?

Accepted Answer

A $p$ orbital has a dumbbell shape and contains a nodal plane.

Question 15

Which of the following is a correct set of quantum numbers for a $3d$ electron?

Accepted Answer

$n=3,\ l=2,\ m_l=1$

Question 16

A sodium streetlamp emits yellow light at $589\ \mathrm{nm}$. What is the energy of a single photon of this light? ($h = 6.626 	imes 10^{-34}\ \mathrm{J\cdot s}$, $c = 3.00 	imes 10^8\ \mathrm{m/s}$)

Accepted Answer

$3.38 	imes 10^{-19}\ \mathrm{J}$

Question 17

Which principle states that no two electrons in an atom can have the same set of four quantum numbers?

Accepted Answer

Pauli Exclusion Principle

Question 18

Which of the following best explains why the Bohr model fails for multi-electron atoms?

Accepted Answer

It does not account for electron-electron repulsions and the resulting splitting of energy levels.

Question 19

How many possible values of $m_l$ are there for $l=2$?

Accepted Answer

5

Question 20

Which of the following is a real-world application of the quantum mechanical model of the atom?

Accepted Answer

Night vision devices using gallium arsenide (GaAs) intensifiers to amplify low levels of light.

Quantum-Mechanical Model of the Atom: Electromagnetic Radiation and Wave Properties

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