Q: A metal surface has a work function $$E_0 = 4.28$$\ \text{eV}$$. What is the minimum frequency of light required to eject electrons from this surface? (Planck's constant h = 4.14$$ \times $$10^{-15}$$\ \text{eV} \cdot \text{s}$$)

$$f_0 = 1.03$$ \times $$10^{15}$$\ \text{Hz}$$

Q: A red laser pointer emits light at $$\lambda = 650\ \text{nm}$$ with a power of $$2.0\ \text{mW}. $$How many photons does it emit per second? ($$h = 6.63 \times 10$$^{-34}$$\ \text{J} \cdot \text{s}$$, $$c = 3.00 \times 10^8$\ \text{m/s})$$

$$6.5 \times 10$$^{15}$$ photons/s

Q: According to Bohr’s model, what is the energy of the $$nth $$stationary state of the hydrogen atom?

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

Question 1

Which of the following statements best describes the concept of quantization as it applies to energy in quantum physics?

Accepted Answer

Energy can only take on certain discrete values, not a continuous range.

Question 2

According to the photon model of light, what is the energy of a single photon with frequency $$f$$?

Accepted Answer

$$E = hf$$

Question 3

A metal surface has a work function $$E_0 = 4.28$$\ 	ext{eV}$$. What is the minimum frequency of light required to eject electrons from this surface? (Planck's constant h = 4.14$$ 	imes $$10^{-15}$$\ 	ext{eV} \cdot 	ext{s}$$)

Accepted Answer

$$f_0 = 1.03$$ 	imes $$10^{15}$$\ 	ext{Hz}$$

Question 4

Which experimental observation directly supports the photon model of light?

Accepted Answer

The photoelectric effect, where electrons are ejected only if the light frequency exceeds a threshold.

Question 5

A red laser pointer emits light at $$\lambda = 650\ 	ext{nm}$$ with a power of $$2.0\ 	ext{mW}. $$How many photons does it emit per second? ($$h = 6.63 	imes 10$$^{-34}$$\ 	ext{J} \cdot 	ext{s}$$, $$c = 3.00 	imes 10^8$\ 	ext{m/s})$$

Accepted Answer

$$6.5 	imes 10$$^{15}$$ photons/s

Question 6

Which equation gives the de Broglie wavelength of a particle of mass $$m$$ and speed $$v$$?

Accepted Answer

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

Question 7

In the photoelectric effect, what happens if the frequency of incident light is below the threshold frequency $$f_0$$?

Accepted Answer

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

Question 8

A particle of mass $$m is $$confined in a one-dimensional box of length $$L. $$What are the allowed energy levels for this particle?

Accepted Answer

$$E_n = \frac{n^2$ h^2$}{8mL^2$}$$, where $$n = 1,2,3,...$$

Question 9

Which of the following best explains why the energy levels of an electron in a hydrogen atom are negative?

Accepted Answer

The electron is bound to the nucleus, and energy must be supplied to remove it.

Question 10

According to Bohr’s model, what is the energy of the $$nth $$stationary state of the hydrogen atom?

Accepted Answer

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

Question 11

A photon is emitted when an electron in a hydrogen atom transitions from $$n=3 to$$ $$n=2. $$Which equation gives the wavelength of the emitted photon?

Accepted Answer

$$\frac{1}{\lambda} = R \left( \frac{1}{2^2$} - \frac{1}{3^2$} \right)$$, where $$R is $$the Rydberg constant

Question 12

Which of the following is a direct consequence of the quantization of angular momentum in the Bohr model?

Accepted Answer

Electrons can only occupy certain allowed orbits with specific radii.

Question 13

Compton scattering demonstrates that photons have which property?

Accepted Answer

Momentum

Question 14

If the stopping potential for a certain metal is measured to be $$2.0\ 	ext{V}$$ when illuminated with light of frequency $$8.0 	imes 10$$^{14}$$\ 	ext{Hz}$$, what is the work function $$E_0 of $$the metal? ($$h = 6.63 	imes 10$$^{-34}$$\ 	ext{J} \cdot 	ext{s}$$, $$e = 1.60 	imes 10$$^{-19}$$\ 	ext{C})$$

Accepted Answer

$$E_0 = hf - eV$$_{stop} = (6.63 	imes $$10^{-34}$$ 	imes 8.0 	imes $$10^{14}) - (1.60$$ 	imes $$10^{-19}$$ 	imes 2.0) = 3.30 	imes $$10^{-19}$$\ 	ext{J}$$

Question 15

Which of the following best describes the difference between photon absorption and collisional excitation in atoms?

Accepted Answer

Photon absorption involves absorbing a photon's energy, while collisional excitation involves energy transfer from a colliding particle.

Question 16

A particle in a box of length $$L is in $$its second excited state. What is the quantum number $$n$$ for this state?

Accepted Answer

$$n = 3$$

Question 17

Which of the following is NOT a postulate of the photon model of light?

Accepted Answer

Each photon has a mass proportional to its energy.

Question 18

Which real-world application relies on the quantization of energy levels in atoms?

Accepted Answer

The emission spectra of elements used in identifying chemical compositions of stars.

Question 19

Which of the following best explains why the photoelectric effect cannot be explained by classical wave theory?

Accepted Answer

Classical theory predicts that increasing light intensity should always eject electrons, regardless of frequency.

Chapter 38: Quantization – Study Notes for Physics with Calculus

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