Q: A star emits blackbody radiation with a peak wavelength of $$700\ \text{nm}. $$What is its surface temperature? (Use $$\lambda_{max} T = 2.898 \times 10$$^{-3}$$\ \text{m} \cdot \text{K})$$

$$T = \frac{2.898 \times 10$$^{-3}$$}{700 \times 10$$^{-9}$$} = 4140\ \text{K}$$

Q: A metal has a work function $$W_0 = 2.5$$\ \text{eV}$$. What is the minimum frequency of light required to eject electrons from its surface? (h = 6.63$$ \times $$10^{-34}$$\ \text{J} \cdot \text{s}$$, 1$$\ \text{eV} = 1.60 \times $$10^{-19}$$\ \text{J}$$)

$$f_0$$ = \frac{$$W_0$$}{h} = \frac{2.5 \times 1.60 \times $$10^{-19}$$}{6.63 \times $$10^{-34}$$} = 6.03 \times $$10^{14}$$\ \text{Hz}$$

Q: A blue photon has a wavelength of $$470\ \text{nm}. $$What is its momentum? ($$h = 6.63 \times 10$$^{-34}$$\ \text{J} \cdot \text{s})$$

$$p = \frac{h}{\lambda} = \frac{6.63 \times 10$$^{-34}$$}{470 \times 10$$^{-9}$$} = 1.41 \times 10$$^{-27}$$\ \text{kg} \cdot \text{m}/\text{s}$$

Q: A solar sail with mass per area $$\sigma = 3.00 \times 10$$^{-3}$$\ \text{kg}/\text{m}^2 is $$illuminated by sunlight of intensity $$I_{Sun} = 1.01 \times 10^6$\ \text{W}/\text{m}^2$$ and average wavelength $$500\ \text{nm}. $$What is the acceleration of the sail? (Assume all photon momentum is absorbed.)

$$a = \frac{I_{Sun}}{\sigma c} = \frac{1.01 \times 10^6$}{3.00 \times 10$$^{-3}$$ \times 3.00 \times 10^8$} = 1.12\ \text{m}/\text{s}^2$$

Q: A neutron (mass $$1.67 \times 10$$^{-27}$$\ \text{kg}) is to be $$diffracted by a crystal with interatomic spacing $$1.00 \times 10$$^{-10}$$\ \text{m}. $$What kinetic energy should the neutron have? ($$h = 6.63 \times 10$$^{-34}$$\ \text{J} \cdot \text{s})$$

$$KE = \frac{p^2$}{2m} = \frac{(6.63 \times 10$$^{-24}$$)^2$$}{2 \times 1.67 \times $$10^{-27}$$} = 1.32 \times $$10^{-20}$$\ \text{J}$

Question 1

In J.J. Thomson’s e/m experiment, an electron beam passes through perpendicular electric and magnetic fields. If the electric field $$\vec{E}$$ and magnetic field $$\vec{B}$$ are adjusted so that the electron beam is not deflected, which equation correctly relates the electron's velocity $$v to $$the fields?

Accepted Answer

$$v = \frac{E}{B}$$

Question 2

In the Millikan oil drop experiment, the charge of an electron was determined by balancing the gravitational force and the electric force on a charged oil droplet. Which equation represents this balance?

Accepted Answer

$$qE = mg$$

Question 3

A blackbody emits radiation with a peak wavelength $$\lambda_{max}. $$According to Wien’s displacement law, what happens to $$\lambda_{max} as $$the temperature $$T$$ increases?

Accepted Answer

$$\lambda_{max}$$ decreases

Question 4

Which phenomenon could NOT be explained by classical wave theory, leading to the so-called 'ultraviolet catastrophe'?

Accepted Answer

The energy distribution of blackbody radiation at short wavelengths

Question 5

Planck’s hypothesis introduced the idea that energy is quantized. What is the expression for the allowed energies of a blackbody resonator?

Accepted Answer

$$E_n = n h f$$

Question 6

A star emits blackbody radiation with a peak wavelength of $$700\ 	ext{nm}. $$What is its surface temperature? (Use $$\lambda_{max} T = 2.898 	imes 10$$^{-3}$$\ 	ext{m} \cdot 	ext{K})$$

Accepted Answer

$$T = \frac{2.898 	imes 10$$^{-3}$$}{700 	imes 10$$^{-9}$$} = 4140\ 	ext{K}$$

Question 7

Which observation from the photoelectric effect experiment directly contradicts the predictions of classical wave theory?

Accepted Answer

No electrons are emitted below a certain cutoff frequency, regardless of intensity

Question 8

A metal has a work function $$W_0 = 2.5$$\ 	ext{eV}$$. What is the minimum frequency of light required to eject electrons from its surface? (h = 6.63$$ 	imes $$10^{-34}$$\ 	ext{J} \cdot 	ext{s}$$, 1$$\ 	ext{eV} = 1.60 	imes $$10^{-19}$$\ 	ext{J}$$)

Accepted Answer

$$f_0$$ = \frac{$$W_0$$}{h} = \frac{2.5 	imes 1.60 	imes $$10^{-19}$$}{6.63 	imes $$10^{-34}$$} = 6.03 	imes $$10^{14}$$\ 	ext{Hz}$$

Question 9

If light of frequency $$f is $$incident on a metal with work function $$W_0$$, what is the maximum kinetic energy $$KE_{max} of $$the emitted photoelectrons?

Accepted Answer

$$KE_{max} = h f - W_0$

Question 10

A blue photon has a wavelength of $$470\ 	ext{nm}. $$What is its momentum? ($$h = 6.63 	imes 10$$^{-34}$$\ 	ext{J} \cdot 	ext{s})$$

Accepted Answer

$$p = \frac{h}{\lambda} = \frac{6.63 	imes 10$$^{-34}$$}{470 	imes 10$$^{-9}$$} = 1.41 	imes 10$$^{-27}$$\ 	ext{kg} \cdot 	ext{m}/	ext{s}$$

Question 11

A solar sail with mass per area $$\sigma = 3.00 	imes 10$$^{-3}$$\ 	ext{kg}/	ext{m}^2 is $$illuminated by sunlight of intensity $$I_{Sun} = 1.01 	imes 10^6$\ 	ext{W}/	ext{m}^2$$ and average wavelength $$500\ 	ext{nm}. $$What is the acceleration of the sail? (Assume all photon momentum is absorbed.)

Accepted Answer

$$a = \frac{I_{Sun}}{\sigma c} = \frac{1.01 	imes 10^6$}{3.00 	imes 10$$^{-3}$$ 	imes 3.00 	imes 10^8$} = 1.12\ 	ext{m}/	ext{s}^2$$

Question 12

According to de Broglie, what is the wavelength associated with a particle of mass $$m$$ and velocity $$v$$?

Accepted Answer

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

Question 13

A neutron (mass $$1.67 	imes 10$$^{-27}$$\ 	ext{kg}) is to be $$diffracted by a crystal with interatomic spacing $$1.00 	imes 10$$^{-10}$$\ 	ext{m}. $$What kinetic energy should the neutron have? ($$h = 6.63 	imes 10$$^{-34}$$\ 	ext{J} \cdot 	ext{s})$$

Accepted Answer

$$KE = \frac{p^2$}{2m} = \frac{(6.63 	imes 10$$^{-24}$$)^2$$}{2 	imes 1.67 	imes $$10^{-27}$$} = 1.32 	imes $$10^{-20}$$\ 	ext{J}$

Question 14

Which experiment provided direct evidence for the quantization of electric charge?

Accepted Answer

Millikan oil drop experiment

Question 15

Which device in modern technology is based on the photoelectric effect?

Accepted Answer

Charge-coupled device (CCD) in digital cameras

Question 16

In the double-slit experiment with electrons, what is observed on the screen if electrons are sent one at a time?

Accepted Answer

An interference pattern gradually builds up

Question 17

Which statement best describes the wave-particle duality of matter?

Accepted Answer

Particles such as electrons exhibit both wave-like and particle-like properties

Early Quantum Theory and Models of the Atom

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