#1Density of Photons
The red light emitted by a 3.00-mW helium-neon laser has a wavelength of 633 nm. Suppose that the diameter of the laser beam is 1.00 mm. Assuming that the light intensity is uniformly distributed over the cross-sectional area of the beam, calculate the number density of photons in the beam.
#2Photoelectric Effect
The stopping potential for electrons emitted from a metallic surface is found to be 0.710 V when illuminated with monochromatic light of wavelength 491 nm. When monochromatic light from a second source that has a different wavelength than the first source is shone on the metal, the stopping potential is found to be 1.43 V.
a) Determine the wavelength of the second light source.
b) Determine the work function for the metal.
#3 Compton Backscattering
Consider photons that have a wavelength of 0.0711 nm scattering off an electron that is assumed to be at rest.
a) What is the energy of these photons?
b) Determine the wavelength and energy of the photons that are scattered in the direction opposite to the direction of the incoming photons.
#4Particle in a Box
a) Determine the energy of the ground state and the first two excited states of a neutron in a one-dimensional box of length 1.00 x 10–15 m (= 1.00 fm). (This is about the size of an atomic nucleus.)
b) Calculate the wavelength of light emitted when the neutron makes a transition from the n = 2 state to the n = 1 state.
c) Calculate the wavelength of light emitted when the neutron makes a transition from the n = 3 state to the n = 2 state.
d) Calculate the wavelength of light emitted when the neutron makes a transition from the n = 3 state to the n = 1 state.
#5 Neutron deBroglie Wavelength
Neutrons in thermal equilibrium with matter have an average kinetic energy of (3/2)kBT, where kB is the Boltzmann constant and T is the absolute temperature. Take room temperature (T = 300 K) to be the temperature of the environment of the neutrons.
a) Calculate the average kinetic energy of such a neutron in this environment.
b) What is the corresponding de Broglie wavelength of such neutron.
#6 Rectangular Corral
A two-dimensional infinite square well of widths Lx = Land Ly= 2L, contains a particle of mass m. What multiple of E0 (=h2/8mL2) are...
a) the energy of the particle’s ground state.
b) the energy of the particle’s first excited state.
c) the energy of the particle’s lowest degenerate state.
d) the difference between the energies of the particle’s second and third excited states.
#7Probability Density
The wave function of a particle of mass m confined in an infinite 1-D square well of width L = 0.250 nm, is: , for 0 ≤ x ≤ L and everywhere else. The energy of the particle in this state is E = 54.2eV.
a) What is the mass of the particle? Answer in both eV/c2 and kg.)
P(x) is the probability density. That is, P(x)dx is the probability that the particle is between x and x+dx when dx is small.
b) For how many values of x does P(x) = 5 nm–1?
c) What is the largest value of x for which P(x) = 5 nm–1.