Q: A photon of light has a wavelength of $$\lambda = 500\ \mathrm{nm}. $$What is its frequency? (Speed of light $$c = 3.00 \times 10^8$\ \mathrm{m/s})$$

$$6.00 \times 10$$^{14}$$\ \mathrm{Hz}$$

Q: What is the energy (in joules) of a single photon with a frequency of $$8.0 \times 10$$^{14}$$\ \mathrm{Hz}$$? (Planck's constant $$h = 6.626 \times 10$$^{-34}$$\ \mathrm{J \cdot s})$$

$$5.30 \times 10$$^{-19}$$\ \mathrm{J}$$

Q: For a hydrogen-like ion with $$Z=3 (Li$^{2+}$$), what is the energy (in J) of the electron in the $$n=2$$ level? ($$E_n = -2.18 \times 10$$^{-18}$$\ \mathrm{J} \times \frac{Z^2$}{n^2$})$$

$$-9.81 \times 10$$^{-18}$$\ \mathrm{J}$$

Question 1

Which of the following best describes the phenomenon of 'wave-particle duality' as it applies to electrons?

Accepted Answer

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

Question 2

A photon of light has a wavelength of $$\lambda = 500\ \mathrm{nm}. $$What is its frequency? (Speed of light $$c = 3.00 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$6.00 	imes 10$$^{14}$$\ \mathrm{Hz}$$

Question 3

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

Accepted Answer

The double-slit experiment with electrons

Question 4

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

Accepted Answer

The atom emits a photon with energy equal to the difference between the two levels.

Question 5

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

Accepted Answer

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

Question 6

What is the energy (in joules) of a single photon with a frequency of $$8.0 	imes 10$$^{14}$$\ \mathrm{Hz}$$? (Planck's constant $$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J \cdot s})$$

Accepted Answer

$$5.30 	imes 10$$^{-19}$$\ \mathrm{J}$$

Question 7

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

Accepted Answer

Electrons can occupy only certain energy levels, and photons are emitted when electrons transition between these levels.

Question 8

Calculate the wavelength (in nm) of light emitted when an electron in a hydrogen atom falls from $$n=3 to$$ $$n=2$$. ($$R_H = 1.097 	imes 10^7$\ \mathrm{m}^{-1})$$

Accepted Answer

$$656\ \mathrm{nm}$$

Question 9

Which quantum numbers describe a 4d orbital?

Accepted Answer

$$n=4,\ l=2$$

Question 10

How many possible values of the magnetic quantum number $$m_l$$ are there for an $$f$$ orbital?

Accepted Answer

7

Question 11

Which of the following statements about the Heisenberg Uncertainty Principle is correct?

Accepted Answer

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

Question 12

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 13

Which of the following orbitals has the greatest penetration to the nucleus in a multi-electron atom?

Accepted Answer

2s

Question 14

What is the maximum number of electrons that can occupy the $$n=3$$ shell?

Accepted Answer

18

Question 15

Which of the following electron configurations represents a paramagnetic atom?

Accepted Answer

$$1s^2$$\ $$2s^2$$\ $$2p^3$$

Question 16

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 17

For a hydrogen-like ion with $$Z=3 (Li$^{2+}$$), what is the energy (in J) of the electron in the $$n=2$$ level? ($$E_n = -2.18 	imes 10$$^{-18}$$\ \mathrm{J} 	imes \frac{Z^2$}{n^2$})$$

Accepted Answer

$$-9.81 	imes 10$$^{-18}$$\ \mathrm{J}$$

Question 18

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

Accepted Answer

Constructive interference increases amplitude, while destructive interference decreases or cancels amplitude.

Question 19

Which of the following is the correct electron configuration for the Sn$$^{2+}$$ ion?

Accepted Answer

$$[Kr]\ 5s^2$\ 4d$$^{10}$$\ 5p^0$

Question 20

Which of the following statements about orbital shapes is correct?

Accepted Answer

s orbitals are spherically symmetric, p orbitals have two lobes, and d orbitals have four lobes (except $$d_{z^2$}).$$

Quantum-Mechanical Model of the Atom: Foundations and Properties of Light

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