Q: The energy levels of the hydrogen atom are given by which of the following formulas?

$$E_n = -\dfrac{13.60\ \text{eV}}{n^2$}$$

Q: For a hydrogen atom, what is the value of the Bohr radius $$a_0$$?

$$a_0 = 5.29$$ \times $$10^{-11}$$\ \text{m}$$

Question 1

Which of the following best describes the potential energy function for the electron in a hydrogen atom according to quantum mechanics?

Accepted Answer

$$U(r) = -\dfrac{1}{4\pi\$$varepsilon_0$$} \dfrac{e^2$}{r}$$

Question 2

The energy levels of the hydrogen atom are given by which of the following formulas?

Accepted Answer

$$E_n = -\dfrac{13.60\ 	ext{eV}}{n^2$}$$

Question 3

For a hydrogen atom, what is the value of the Bohr radius $$a_0$$?

Accepted Answer

$$a_0 = 5.29$$ 	imes $$10^{-11}$$\ 	ext{m}$$

Question 4

Which quantum number determines the shape of the orbital in the hydrogen atom?

Accepted Answer

Orbital angular momentum quantum number $$l$$

Question 5

What is the maximum number of electrons that can occupy the $$3d$$ subshell?

Accepted Answer

10

Question 6

Which of the following statements about the Zeeman effect is correct?

Accepted Answer

It is the splitting of atomic energy levels in the presence of a magnetic field.

Question 7

What is the allowed range of values for the magnetic quantum number $$m_l$$ for an electron in a $$d$$ orbital ($$l=2$$)?

Accepted Answer

$$m_l = 0, \pm1, \pm2$$

Question 8

According to the Pauli exclusion principle, which of the following is true for electrons in an atom?

Accepted Answer

No two electrons can have the same values of all four quantum numbers ($$n$$, $$l$$, $$m_l$$, $$m_s).$$

Question 9

What is the magnitude of the orbital angular momentum for an electron in a hydrogen atom with $$l=3$$?

Accepted Answer

$$L = \sqrt{l(l+1)}\hbar = \sqrt{12}\hbar = 2\sqrt{3}\hbar$$

Question 10

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

Accepted Answer

$$n=2 \rightarrow n=1$$

Question 11

In the Stern-Gerlach experiment, what was the key evidence for the existence of electron spin?

Accepted Answer

The beam split into two distinct spots.

Question 12

What is the value of the spin quantum number $$s$$ for an electron?

Accepted Answer

$$s = \dfrac{1}{2}$$

Question 13

Which of the following is the correct expression for the energy of interaction between the magnetic moment of an electron and an external magnetic field $$B ($$Zeeman effect)?

Accepted Answer

$$U = -\vec{\mu} \cdot \vec{B}$$

Question 14

For a hydrogen atom, which quantum numbers are needed to uniquely specify an electron state?

Accepted Answer

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

Question 15

Which of the following best explains why the $$2s$$ electron in a lithium atom experiences a net nuclear charge of approximately $$+e$$?

Accepted Answer

Because the $$2s$$ electron is shielded by the two $$1s$$ electrons, reducing the effective nuclear charge.

Question 16

According to the selection rules for electric dipole transitions in the hydrogen atom, which of the following transitions is allowed?

Accepted Answer

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

Question 17

What is the physical significance of the radial probability distribution function $$P(r)$$ for the hydrogen atom?

Accepted Answer

It gives the probability per unit radial length of finding the electron at a distance $$r$$ from the nucleus.

Question 18

Which of the following best describes the effect of screening in many-electron atoms?

Accepted Answer

Screening decreases the effective nuclear charge experienced by outer electrons.

Question 19

According to Moseley's law, the frequency of the $$K_\alpha x-$$ray line is related to the atomic number $$Z by $$which formula?

Accepted Answer

$$f = 2.48 	imes 10$$^{15}$$\ 	ext{Hz} \cdot (Z-1)^2$

Quantum Mechanics II: The Hydrogen Atom and Many-Electron Atoms

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