$E_n = - \frac{13.6}{n^2} \, \text{eV}$

Question 1

Which of the following best explains why the photoelectric effect provided evidence for the quantization of energy in light?

Accepted Answer

Electrons are emitted only when the frequency of light exceeds a threshold, regardless of intensity.

Question 2

According to the Bohr model, what is the expression for the energy of the nth orbit of the hydrogen atom?

Accepted Answer

$E_n = - \frac{13.6}{n^2} \, 	ext{eV}$

Question 3

A hydrogen atom makes a transition from $n=4$ to $n=2$. What is the wavelength of the photon emitted? (Use $R_H = 1.097 	imes 10^7 \, 	ext{m}^{-1}$)

Accepted Answer

$\lambda = \frac{1}{R_H \left( \frac{1}{2^2} - \frac{1}{4^2} \right)}$

Question 4

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Azimuthal (angular momentum) quantum number $l$

Question 5

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

Accepted Answer

18

Question 6

Which of the following statements about the Heisenberg uncertainty principle is correct?

Accepted Answer

It states that the more precisely the position is known, the less precisely the momentum is known.

Question 7

Which experiment demonstrated the wave nature of electrons?

Accepted Answer

Double-slit experiment with electrons

Question 8

What is the de Broglie wavelength of an electron with momentum $p$?

Accepted Answer

$\lambda = \frac{h}{p}$

Question 9

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 10

Which of the following best describes the limitation of the Bohr model of the atom?

Accepted Answer

It does not account for the wave nature of electrons.

Question 11

What is the physical meaning of the square of the wave function $|\psi|^2$ in quantum mechanics?

Accepted Answer

It gives the probability density of finding the electron at a point.

Question 12

Which quantum number is associated with the orientation of an orbital in space?

Accepted Answer

Magnetic quantum number $m_l$

Question 13

How many possible values of $m_l$ are there for $l=2$?

Accepted Answer

5

Question 14

Which of the following statements about $d$ orbitals is correct?

Accepted Answer

There are five $d$ orbitals, each with a different orientation.

Question 15

Which quantum number is responsible for the spin of an electron?

Accepted Answer

Spin quantum number $m_s$

Question 16

A spectral line in the hydrogen atom is observed at $486 \ 	ext{nm}$. To which series does this line belong?

Accepted Answer

Balmer series

Question 17

Which of the following is a correct statement about the relationship between quantum numbers?

Accepted Answer

$l$ can take values from $0$ to $n-1$

Question 18

Which of the following best describes the shape of a $p$ orbital?

Accepted Answer

Dumbbell-shaped

Question 19

If an electron in a hydrogen atom transitions from $n=5$ to $n=2$, what happens?

Accepted Answer

A photon is emitted and the atom moves to a lower energy state.

Question 20

Which of the following is a limitation of the Bohr model that is addressed by quantum mechanics?

Accepted Answer

The Bohr model cannot explain the spectra of multi-electron atoms.

Quantum-Mechanical Model of the Hydrogen Atom: Key Concepts and Applications

Study Guide - Practice Questions