Q: A photon of green light has a wavelength of 520 nm. What is the energy of a single photon? (Use $h = 6.626 \times 10^{-34}$ J·s and $c = 3.00 \times 10^8$ m/s)

$E = \dfrac{hc}{\lambda} = \dfrac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{520 \times 10^{-9}} \approx 3.82 \times 10^{-19}$ J

Q: What is the energy of a photon emitted when an electron in a hydrogen atom relaxes from $n=4$ to $n=2$? Use $E_{\text{photon}} = 2.18 \times 10^{-18} \left[ \dfrac{1}{n_{\text{final}}^2} - \dfrac{1}{n_{\text{initial}}^2} \right]$ J.

$E = 2.18 \times 10^{-18} \left[ \dfrac{1}{2^2} - \dfrac{1}{4^2} \right] = 4.09 \times 10^{-19}$ J

Question 1

Which of the following statements best describes the quantum-mechanical model of the atom?

Accepted Answer

It provides a probability map for the location and energy of electrons in atoms and molecules.

Question 2

Which equation correctly relates the wavelength $\lambda$ and frequency $
u$ of electromagnetic radiation?

Accepted Answer

$c = \lambda 
u$

Question 3

A photon of green light has a wavelength of 520 nm. What is the energy of a single photon? (Use $h = 6.626 	imes 10^{-34}$ J·s and $c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$E = \dfrac{hc}{\lambda} = \dfrac{6.626 	imes 10^{-34} 	imes 3.00 	imes 10^8}{520 	imes 10^{-9}} \approx 3.82 	imes 10^{-19}$ J

Question 4

Which experiment provided evidence for the particle nature of light?

Accepted Answer

The photoelectric effect

Question 5

What is the energy of a photon emitted when an electron in a hydrogen atom relaxes from $n=4$ to $n=2$? Use $E_{	ext{photon}} = 2.18 	imes 10^{-18} \left[ \dfrac{1}{n_{	ext{final}}^2} - \dfrac{1}{n_{	ext{initial}}^2} ight]$ J.

Accepted Answer

$E = 2.18 	imes 10^{-18} \left[ \dfrac{1}{2^2} - \dfrac{1}{4^2} ight] = 4.09 	imes 10^{-19}$ J

Question 6

Which quantum number primarily determines the size and energy of an orbital?

Accepted Answer

Principal quantum number $n$

Question 7

For $n=4$, what are the possible values of the angular momentum quantum number $\ell$?

Accepted Answer

$\ell = 0, 1, 2, 3$

Question 8

How many orbitals are present in the $3d$ subshell?

Accepted Answer

5

Question 9

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

Accepted Answer

$n=2, \ell=2, m_\ell=0, m_s=+\frac{1}{2}$

Question 10

Which quantum number describes the orientation of an orbital in space?

Accepted Answer

Magnetic quantum number $m_\ell$

Question 11

How many electrons can occupy all the orbitals in the $n=3$ shell?

Accepted Answer

18

Question 12

Which of the following best explains why atomic emission spectra consist of discrete lines?

Accepted Answer

Energy changes of electrons are quantized; only specific transitions are allowed.

Question 13

Which quantum number differentiates between the two electrons in the same orbital?

Accepted Answer

Spin quantum number $m_s$

Question 14

Which of the following is a correct set of quantum numbers for an electron in a $4f$ orbital?

Accepted Answer

$n=4, \ell=3, m_\ell=+2, m_s=+\frac{1}{2}$

Question 15

Which statement about the $p$ orbitals is correct?

Accepted Answer

$p$ orbitals begin at $n=2$ and have three orientations.

Question 16

If $n=5$, what is the maximum value of $\ell$ and how many orbitals are in that subshell?

Accepted Answer

Maximum $\ell=4$ (g), with 9 orbitals

Question 17

Which of the following is true about the $d$ orbitals?

Accepted Answer

$d$ orbitals begin at $n=3$ and have five orientations.

Question 18

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

Accepted Answer

Pauli Exclusion Principle

Quantum-Mechanical Model of the Atom & Periodic Properties: Study Notes

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