Question 1

Which experiment led to the discovery of the atomic nucleus, and what was the key observation that supported this discovery?

Accepted Answer

The Gold Foil Experiment; most alpha particles passed through, but some were deflected at large angles.

Question 2

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

Accepted Answer

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

Question 3

Which of the following best explains why the photoelectric effect could not be explained by classical physics?

Accepted Answer

Electrons were only ejected when the incident light exceeded a threshold frequency, regardless of intensity.

Question 4

According to Planck’s quantum theory, the energy of a photon is given by which equation?

Accepted Answer

$$E = h
u$$

Question 5

A photon with a wavelength of 242.4 nm is absorbed by an O$$_2$$ molecule. What is the energy of one photon? (Planck’s constant $$h = 6.626 	imes 10$$^{-34}$$ J·s, c = 3.00$$ 	imes $$10^8 m/s)$$

Accepted Answer

$$8.20 	imes 10$$^{-19}$$ J

Question 6

Which of the following statements about atomic emission spectra is correct?

Accepted Answer

Each element has a unique line spectrum because its electrons occupy quantized energy levels.

Question 7

The Balmer series in the hydrogen spectrum corresponds to electronic transitions ending at which principal quantum number?

Accepted Answer

$$n = 2$$

Question 8

Calculate the wavelength of the photon emitted when an electron in a hydrogen atom transitions from $$n = 5 to$$ $$n = 2. ($$Rydberg constant $$R_H = 2.179 	imes 10$$^{-18}$$ J, h = 6.626$$ 	imes $$10^{-34} J$$·s, $$c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$$434 nm$$

Question 9

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number ($$\ell)$$

Question 10

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

Accepted Answer

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

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 a particle.

Question 12

For a particle in a one-dimensional box of length $$L$$, what is the energy of the $$nth $$quantum state?

Accepted Answer

$$E_n = \frac{n^2$ h^2$}{8mL^2$}$$

Question 13

Which of the following statements about the Schrödinger equation for the hydrogen atom is correct?

Accepted Answer

It can be solved exactly only for hydrogen and hydrogen-like ions.

Question 14

Which orbital designation corresponds to the quantum numbers $$n = 4, \ell = 2, m_\ell = 0$$?

Accepted Answer

4d

Question 15

In a multi-electron atom, which of the following orbitals experiences the greatest effective nuclear charge ($$Z_{	ext{eff}}$$)?

Accepted Answer

1s

Question 16

Which of the following correctly ranks the orbitals in order of increasing shielding effect?

Accepted Answer

d \u003c p \u003c s

Question 17

Which real-world application relies on the unique line spectra of elements for identification?

Accepted Answer

Flame tests in forensic analysis

Question 18

What is the de Broglie wavelength of an electron traveling at $$1.0 	imes 10^7$ m/s? (Mass of electron m = 9.11$$ 	imes $$10^{-31} kg$$, $$h = 6.626 	imes 10$$^{-34}$$ J·s)

Accepted Answer

$$7.28 	imes 10$$^{-8}$$ m

Question 19

Which of the following best describes the concept of orbital penetration?

Accepted Answer

The ability of an electron in an orbital to get close to the nucleus, increasing its effective nuclear charge.

Atoms: The Quantum World – Electronic Structure and Atomic Theory

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