Q: Which formula would you use to calculate the energy of a photon emitted when an electron transitions from a higher energy level $$n_i to a $$lower energy level $$n_f in a $$hydrogen atom?

$$E_{photon} = (2.1799 \text{ aJ}) \left( \dfrac{1}{n_f^2$} - \dfrac{1}{n_i^2$} \right)$$

Q: A photon is emitted when an electron in a hydrogen atom transitions from $$n=4 to$$ $$n=2. $$What is the energy of the emitted photon in attojoules (aJ)?

$$E_{photon} = (2.1799 \text{ aJ}) \left( \dfrac{1}{2^2$} - \dfrac{1}{4^2$} \right) = 2.1799 \text{ aJ} \left( \dfrac{1}{4} - \dfrac{1}{16} \right) = 2.1799 \text{ aJ} \left( \dfrac{4-1}{16} \right) = 2.1799 \text{ aJ} \times 0.1875 = 0.409 aJ$$

Q: A metal has a work function $$\Phi = 2.0 \text{ eV}. If $$light of frequency $$\nu$$ such that $$h\nu = 3.0 \text{ eV} is $$shone on it, what is the kinetic energy of the ejected electron?

$$E_k = h\nu - \Phi = 3.0 \text{ eV} - 2.0 \text{ eV} = 1.0 \text{ eV}$$

Question 1

Which equation describes the wavelength of a particle according to de Broglie's hypothesis?

Accepted Answer

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

Question 2

According to Bohr’s model, which of the following statements is TRUE about the energy levels of the hydrogen atom?

Accepted Answer

The energy levels are quantized and depend only on the principal quantum number $$n.$$

Question 3

Which formula would you use to calculate the energy of a photon emitted when an electron transitions from a higher energy level $$n_i to a $$lower energy level $$n_f in a $$hydrogen atom?

Accepted Answer

$$E_{photon} = (2.1799 	ext{ aJ}) \left( \dfrac{1}{n_f^2$} - \dfrac{1}{n_i^2$} ight)$$

Question 4

Which of the following best explains why Bohr’s model is limited in its application?

Accepted Answer

It only accurately describes one-electron systems like hydrogen.

Question 5

A photon is emitted when an electron in a hydrogen atom transitions from $$n=4 to$$ $$n=2. $$What is the energy of the emitted photon in attojoules (aJ)?

Accepted Answer

$$E_{photon} = (2.1799 	ext{ aJ}) \left( \dfrac{1}{2^2$} - \dfrac{1}{4^2$} ight) = 2.1799 	ext{ aJ} \left( \dfrac{1}{4} - \dfrac{1}{16} ight) = 2.1799 	ext{ aJ} \left( \dfrac{4-1}{16} ight) = 2.1799 	ext{ aJ} 	imes 0.1875 = 0.409 aJ$$

Question 6

Which equation would you use to calculate the kinetic energy of an electron ejected from a metal surface in the photoelectric effect?

Accepted Answer

$$E_k = h 
u - \Phi$$

Question 7

If the momentum of an electron is doubled, what happens to its de Broglie wavelength?

Accepted Answer

The wavelength is halved.

Question 8

Which of the following is a key difference between classical and quantum models of the atom?

Accepted Answer

Quantum models predict discrete energy levels, while classical models predict continuous energy.

Question 9

A student claims that Bohr’s model can be used to predict the energy levels of a helium atom. Is this claim correct?

Accepted Answer

No, because Bohr’s model only works for one-electron systems.

Question 10

Which equation would you use to relate the frequency $$
u$$ and wavelength $$\lambda of $$electromagnetic radiation?

Accepted Answer

$$c = \lambda 
u$$

Question 11

Which of the following best describes the significance of the equation $$E_n = -2.18 	imes 10$$^{-18}$$ 	ext{ J} \left( \dfrac{1}{n^2$} ight)$$?

Accepted Answer

It gives the energy of an electron in the $$nth $$energy level of a hydrogen atom.

Question 12

Which quantum mechanical concept explains why electrons cannot have arbitrary energies in atoms?

Accepted Answer

Energy quantization

Question 13

A metal has a work function $$\Phi = 2.0 	ext{ eV}. If $$light of frequency $$
u$$ such that $$h
u = 3.0 	ext{ eV} is $$shone on it, what is the kinetic energy of the ejected electron?

Accepted Answer

$$E_k = h
u - \Phi = 3.0 	ext{ eV} - 2.0 	ext{ eV} = 1.0 	ext{ eV}$$

Question 14

Which of the following is NOT a limitation of Bohr’s atomic model?

Accepted Answer

It accurately predicts the energy levels of all atoms.

Question 15

Which equation would you use to calculate the velocity of a particle given its de Broglie wavelength?

Accepted Answer

$$\lambda = \dfrac{h}{mv}$$

Question 16

If an electron in a hydrogen atom moves from $$n=3 to$$ $$n=1$$, what happens to the energy of the atom?

Accepted Answer

The atom loses energy and emits a photon.

Question 17

Which of the following equations is used to calculate the kinetic energy of a moving particle?

Accepted Answer

$$E_k = \dfrac{1}{2}mv^2$

Question 18

Which concept is illustrated by the inability to know both the position and energy of an electron exactly, as noted in quantum mechanics?

Accepted Answer

Heisenberg uncertainty principle

Question 19

Which equation would you use to calculate the frequency of light given its wavelength?

Accepted Answer

$$
u = \dfrac{c}{\lambda}$$

Quantum Theory, Atomic Structure, and Key Equations in General Chemistry

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