Quantum Physics and Wave Optics Problem Set
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Wave Optics and Interference
1. Double Slit Experiment Maxima
A double slit experiment is performed with sodium light (λ = 589.0 nm). The slits are separated by 1.14 mm and the screen is 2.336 m from the slits. Find the separation between adjacent maxima on the screen.
Photons and the Photoelectric Effect
2. Photon Energy and Wavelength
What is the wavelength of an X-ray photon of energy 10.9 keV? What is the wavelength of a gamma ray photon of energy 1.19 MeV? What is the range of energies of photons of visible light with wavelengths 350 nm to 700 nm?
3. Zinc Surface Cutoff Wavelength
What is the cutoff wavelength for the photoelectric effect using a zinc surface?
4. Stopping Potential Calculations
A metal surface has a photoelectric cutoff wavelength of 340.3 nm. It is illuminated with light of wavelength 242.4 nm. What is the stopping potential?
For wavelengths below the cutoff wavelength λthreshold, the photons possess enough energy to free electrons from the metal with some energy left over (which becomes the photoelectron kinetic energy).
The stopping potential Vs is the minimum voltage required to stop the flow of all photoelectrons emitted from the metal.
This voltage will create a potential barrier of height eVs. When the height of this barrier is equal to Kmax of all photoelectrons, none will be able to overcome this potential barrier and no current will flow. Therefore, the stopping potential and Kmax are related by:
Blackbody Radiation and Astrophysics
5. Cosmic Microwave Background
The universe is filled with thermal radiation, which has a blackbody spectrum at an effective temperature of 2.7 K. What is the peak wavelength of this radiation? What is the energy of the photons at the peak wavelength?
10. COBE Satellite Data Analysis
The COBE satellite was launched in 1969 to study the cosmic background radiation and measure its temperature.
By measuring at many different wavelengths, researchers were able to show that the background radiation exactly followed the spectral distribution expected for a black body.
At a wavelength of λ = 0.144 cm, the radiant intensity is I = 1.47E-7 W/m2 in a wavelength interval of Δλ = 0.0072 cm. What is the temperature of the radiation that would be deduced from this data?
Scattering and Atomic Recoil
6. Compton Scattering Energy
Incident photons of energy 10.19 keV are Compton scattered, and the scattered beam is observed at 175.65 degrees relative to the incident beam. What is the energy of the scattered photons at that angle?
What is the kinetic energy of the recoiling electrons?
7. Silver Atom Recoil Momentum
Suppose an atom of silver at rest emits an X-ray photon of energy 7.2 keV. Calculate the magnitude of the recoil momentum of the atom. Assume the mass of the silver atom is 108u (1u = 931 MeV/c2).
Calculate the magnitude of the recoil kinetic energy of the atom.
X-ray Production and Photon Emission
8. Bremsstrahlung Minimum Wavelength
What is the minimum X-ray wavelength produced in Bremsstrahlung by electrons that have been accelerated through 2.36E4 V?
The minimum wavelength corresponds to the maximum energy. Photons with the maximum energy will be produced when the electrons are stopped completely through a single collision, and all of their kinetic energy (eΔV) is used to produce a single photon.
9. Light Bulb Photon Emission Rate
A certain green light bulb emits at a single wavelength of λ = 550 nm. It consumes P = 65 W of electrical power and is ε = 71% efficient in converting electrical energy into light. How many photons does the bulb emit in one hour?
Momentum Transfer
11. Hydrogen Atom Velocity Change
A hydrogen atom is moving at a speed of v = 100 m/s. It absorbs a photon of wavelength λ = 150 nm that is moving in the opposite direction. What is the change in velocity of the atom as a result of absorbing the photon?
