PHYS 3310 Module 3 Self Assessment Practice Problems

Module 3 Self Assessment Practice Problems

3.1
The universe is filled with thermal radiation, which has a blackbody spectrum at an effective temperature of 2.7 K.
(a) What is the peak wavelength of this radiation?
(b) What is the energy (in eV) of quanta at the peak wavelength?
(c) In what region of the electromagnetic spectrum is this peak wavelength?
Answer: (a) 1.1 mm (b) 1.16 meV (c) microwave

3.2
A 200-W heater emits a 1.5-µm radiation.
(a) What value of the energy quantum does it emit?
(b) Assuming that the specific heat of a 4.0-kg body is 0.83 kcal/kg·K, how many of these photons must be absorbed by the body to increase its temperature by 2 K?
Answer: (a) 0.82 eV (b) 2.1 x 10²³ quanta

3.3
The photoelectric work function of potassium is 2.1 eV. If light that has a wavelength of 140 nm falls on potassium,
(a) Find the stopping potential for light of this wavelength.
(b) Find the kinetic energy, in electron volts, of the most energetic electrons ejected.
(c) Find the speeds of these electrons.
Answer: (a) 6.76 V (b) 6.76 eV (c) 0.00497c = 1.49 x 10⁶ m/s

3.4
In developing night-vision equipment, you need to measure the work function for a metal surface, so you perform a photoelectric-effect experiment. You measure the stopping potential V₀ as a function of the wavelength of the light that is incident on the surface. You get the results: 𝜆 (nm): 100; 120; 140; 160; 180; 200 V₀ (V): 7.53; 5.59; 3.98; 2.92; 2.06; 1.43
(a) Select a way to plot your results so that the data points fall close to a straight line. Using that plot, find the slope and y-intercept of the best-fit straight line to the data.
(b) Use the results of part (a) to calculate Planck’s constant h (as a test of your data) and the work function (in eV) of the surface.
(c) What is the longest wavelength of light that will produce photoelectrons from this surface?
(d) What wavelength of light is required to produce photoelectrons with kinetic energy 10.0 eV?
Answer: (a) y = 1.23 x 10^-6x – 4.7651 (b) 6.56 x 10^-34 J•s; 4.77 eV (c) 260 nm (d) 84 nm

3.5
Estimate the binding energy of electrons in magnesium, given that the wavelength of 337 nm is the longest wavelength that a photon may have to eject a photoelectron from magnesium photoelectrode.
Answer: 3.68 eV

3.6
A 600-nm light falls on a photoelectric surface and electrons with the maximum kinetic energy of 0.17 eV are emitted. Determine
(a) the work function
(b) the cutoff frequency of the surface.
(c) What is the stopping potential when the surface is illuminated with light of wavelength 400 nm?
Answer: (a) 1.9 eV (b) 4.59 x 10¹⁴ Hz (c) 1.2 V

3.7
The cutoff wavelength for the photoelectric effect in a certain metal is 254 nm.
(a) What is the work function for that metal?
(b) Will the photoelectric effect be observed for 𝜆 > 254 nm or for 𝜆 < 254 nm?
Answer: (a) 4.89 eV (b) 𝜆 < 254 nm

3.8
Incident photons of energy 11.32 keV are Compton scattered, and the scattered beam is observed at 62.9° relative to the incident beam.
(a) What is the energy of the scattered photons at that angle?
(b) How much kinetic energy is given to the scattered electron?
Answer: (a) 11.19 keV (b) 0.13 keV

3.9
A photon with wavelength of 0.1110 nm collides with a free electron that is initially at rest. After the collision the wavelength is 0.1135 nm.
(a) What is the kinetic energy of the electron after the collision?
(b) What is its speed?
(c) If the electron is suddenly stopped (for example, in a solid target), all of its kinetic energy is used to create a photon. What is the wavelength of this photon?
Answer: (a) 246 eV (b) 0.031c (c) 5.04 nm

3.10
An incident x-ray photon with a wavelength of 0.0900 nm is scattered in the backward direction from a free electron that is initially at rest.
(a) What is the magnitude of the momentum of the scattered photon?
(b) What is the kinetic energy of the electron after the photon is scattered?
Answer: (a) 13.1 keV/c (b) 704.5 eV