Q: A radio station broadcasts at a frequency of $$102.5\ \text{MHz}. $$What is the wavelength of these radio waves in meters? (Speed of light $$c = 2.998 \times 10^8$\ \text{m/s})$$

$$\lambda = \dfrac{c}{\nu} = \dfrac{2.998 \times 10^8$}{1.025 \times 10^8$} = 2.93\ \text{m}$$

Q: Calculate the energy in kJ/mol of a photon with a wavelength of $$250\ \text{nm}$$. ($$h = 6.626 \times 10$$^{-34}$$\ \text{J}\cdot\text{s}$$, $$c = 2.998 \times 10^8$\ \text{m/s}$$, $$N_A = 6.022 \times 10$$^{23}$$\ \text{mol}^{-1})$$

$$E = \dfrac{hc}{\lambda} \times N_A = \dfrac{6.626 \times 10$$^{-34}$$ \times 2.998 \times 10^8$}{250 \times 10$$^{-9}$$} \times 6.022 \times 10$$^{23}$$ = 478\ \text{kJ/mol}$$

Q: What is the effective nuclear charge ($$Z_{eff}) $$experienced by an outer electron in a multi-electron atom?

$$Z_{eff} = Z_{actual} - \text{electron shielding}$$

Question 1

Which of the following statements best explains why X-rays have higher energy than visible light?

Accepted Answer

X-rays have a shorter wavelength and higher frequency than visible light.

Question 2

A radio station broadcasts at a frequency of $$102.5\ 	ext{MHz}. $$What is the wavelength of these radio waves in meters? (Speed of light $$c = 2.998 	imes 10^8$\ 	ext{m/s})$$

Accepted Answer

$$\lambda = \dfrac{c}{
u} = \dfrac{2.998 	imes 10^8$}{1.025 	imes 10^8$} = 2.93\ 	ext{m}$$

Question 3

Which phenomenon observed in the double-slit experiment provides evidence for the wave-like nature of light?

Accepted Answer

The formation of an interference pattern of bright and dark bands.

Question 4

According to the photoelectric effect, what happens when light of frequency below the threshold frequency shines on a metal surface?

Accepted Answer

No electrons are ejected, regardless of the light's intensity.

Question 5

Calculate the energy in kJ/mol of a photon with a wavelength of $$250\ 	ext{nm}$$. ($$h = 6.626 	imes 10$$^{-34}$$\ 	ext{J}\cdot	ext{s}$$, $$c = 2.998 	imes 10^8$\ 	ext{m/s}$$, $$N_A = 6.022 	imes 10$$^{23}$$\ 	ext{mol}^{-1})$$

Accepted Answer

$$E = \dfrac{hc}{\lambda} 	imes N_A = \dfrac{6.626 	imes 10$$^{-34}$$ 	imes 2.998 	imes 10^8$}{250 	imes 10$$^{-9}$$} 	imes 6.022 	imes 10$$^{23}$$ = 478\ 	ext{kJ/mol}$$

Question 6

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number ($$l)$$

Question 7

How many total orbitals are present in the $$n=3$$ shell?

Accepted Answer

9

Question 8

Which of the following electron configurations represents a particularly stable arrangement due to a half-filled $$d$$ subshell?

Accepted Answer

[Ar] $$4s^1$$ $$3d^5$$

Question 9

Which atom would you expect to have the largest atomic radius?

Accepted Answer

Ba

Question 10

What is the effective nuclear charge ($$Z_{eff}) $$experienced by an outer electron in a multi-electron atom?

Accepted Answer

$$Z_{eff} = Z_{actual} - 	ext{electron shielding}$$

Question 11

Which of the following best describes the Heisenberg uncertainty principle?

Accepted Answer

The product of the uncertainties in position and momentum is always greater than or equal to $$\dfrac{h}{4\pi}.$$

Question 12

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

Accepted Answer

$$n$$, $$l$$, $$m_l$$, and $$m_s$$

Question 13

Which of the following statements about nodes in atomic orbitals is correct?

Accepted Answer

Nodes are regions where the probability of finding an electron is zero.

Question 14

Which of the following transitions in a hydrogen atom would emit light in the visible region (Balmer series)?

Accepted Answer

$$n=3 to$$ $$n=2$$

Question 15

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

Accepted Answer

$$\lambda = \dfrac{h}{mv} = \dfrac{6.626 	imes 10$$^{-34}$$}{9.11 	imes 10$$^{-31}$$ 	imes 2.00 	imes 10^6$} = 3.64 	imes 10$$^{-10}$$\ 	ext{m}$$

Question 16

Which of the following best describes Hund's rule?

Accepted Answer

Electrons occupy degenerate orbitals singly before pairing up.

Question 17

Which of the following elements has an anomalous electron configuration due to a half-filled $$d$$ subshell?

Accepted Answer

Chromium (Cr)

Question 18

Which of the following statements about atomic radius is correct?

Accepted Answer

Atomic radius increases down a group and decreases across a period.

Light, Atomic Structure, and Electron Configuration: Chapter 5 Study Notes

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