Q: A photon has a wavelength of $$500 \ \text{nm}. $$What is its energy in electron volts? ($$h = 6.63 \times 10$$^{-34}$$ \ \text{J} \cdot \text{s}$$, $$c = 3.00 \times 10^8$ \ \text{m/s}$$, $$1 \ \text{eV} = 1.60 \times 10$$^{-19}$$ \ \text{J})$$

$$E = \frac{hc}{\lambda} = 2.48 \ \text{eV}$$

Q: If the work function of a metal is $$3.0 \ \text{eV}$$, what is the threshold frequency for the photoelectric effect? ($$h = 4.14 \times 10$$^{-15}$$ \ \text{eV} \cdot \text{s})$$

$$f_0$$ = \frac{3.0}{4.14 \times $$10^{-15}$$} = 7.25 \times $$10^{14}$$ \ \text{Hz}$$

Question 1

A spaceship travels at $$0.8c$$ relative to Earth. According to special relativity, what is the factor by which time dilates for an astronaut on the spaceship as observed from Earth?

Accepted Answer

$$\gamma = \frac{1}{\sqrt{1 - (0.8)^2$}} = 1.67$$

Question 2

Which experimental result provided the first strong evidence for the quantization of energy?

Accepted Answer

The photoelectric effect

Question 3

According to Bohr's atomic model, what is the expression for the allowed radii of the electron orbits in a hydrogen atom?

Accepted Answer

$$r_n = n^2$ a_0$

Question 4

A photon with energy $$E = 4.0 \ 	ext{eV}$$ strikes a metal with a work function $$\phi = 2.5 \ 	ext{eV}. $$What is the maximum kinetic energy of the emitted electron?

Accepted Answer

$$K_{max} = 1.5 \ 	ext{eV}$$

Question 5

Which of the following best explains why increasing the intensity of light in the photoelectric effect does not increase the maximum kinetic energy of emitted electrons?

Accepted Answer

The energy of each photon depends only on its frequency, not intensity.

Question 6

If the speed of light is $$c$$ and a particle moves at $$0.6c$$, what is its relativistic momentum $$p if $$its rest mass is $$m_0$$?

Accepted Answer

$$p = \frac{m_0$ \cdot 0.6c}{\sqrt{1 - (0.6)^2$}}$$

Question 7

Which statement best describes the significance of the Michelson-Morley experiment for special relativity?

Accepted Answer

It showed that the speed of light is constant in all inertial frames.

Question 8

A moving observer measures the length of a spaceship to be $$60 \ 	ext{m}$$, while the spaceship's proper length is $$75 \ 	ext{m}. $$What is the speed of the spaceship relative to the observer?

Accepted Answer

$$v = c \sqrt{1 - \left(\frac{60}{75}\$$right)^2$$}$$

Question 9

Which of the following is a postulate of Einstein's special relativity?

Accepted Answer

The laws of physics are the same in all inertial frames.

Question 10

Which equation correctly relates the energy and momentum of a photon?

Accepted Answer

$$E = pc$$

Question 11

Explain, in one or two sentences, why the Bohr model could not explain the fine structure of hydrogen spectral lines.

Accepted Answer

The Bohr model does not account for electron spin or relativistic corrections, which are necessary to explain the fine structure.

Question 12

A photon has a wavelength of $$500 \ 	ext{nm}. $$What is its energy in electron volts? ($$h = 6.63 	imes 10$$^{-34}$$ \ 	ext{J} \cdot 	ext{s}$$, $$c = 3.00 	imes 10^8$ \ 	ext{m/s}$$, $$1 \ 	ext{eV} = 1.60 	imes 10$$^{-19}$$ \ 	ext{J})$$

Accepted Answer

$$E = \frac{hc}{\lambda} = 2.48 \ 	ext{eV}$$

Question 13

Which of the following best describes the quantization of angular momentum in Bohr's model?

Accepted Answer

$$L = n \hbar$$

Question 14

If the work function of a metal is $$3.0 \ 	ext{eV}$$, what is the threshold frequency for the photoelectric effect? ($$h = 4.14 	imes 10$$^{-15}$$ \ 	ext{eV} \cdot 	ext{s})$$

Accepted Answer

$$f_0$$ = \frac{3.0}{4.14 	imes $$10^{-15}$$} = 7.25 	imes $$10^{14}$$ \ 	ext{Hz}$$

Question 15

Which of the following is NOT a prediction of special relativity?

Accepted Answer

The speed of light is different in different inertial frames.

Question 16

A stationary muon has a lifetime of $$2.2 \ \mu	ext{s}. If it $$moves at $$0.98c$$, what is its observed lifetime according to an Earth observer?

Accepted Answer

$$	au = \frac{2.2}{\sqrt{1 - (0.98)^2$}} = 11.1 \ \mu	ext{s}$$

Question 17

Which of the following best describes the dual nature of light as revealed by the photoelectric effect?

Accepted Answer

Light behaves as both a wave and a particle.

Question 18

Derive the equation for the energy levels of the hydrogen atom in the Bohr model, starting from the quantization of angular momentum.

Accepted Answer

Using $$L = n\hbar$$ and centripetal force, $$E_n = -\frac{13.6 \ 	ext{eV}}{n^2$}.$$

Physics Study Guide: Relativity, Modern Physics, and Quantization

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