Download Compton Effect and Spectral Lines

Quantum Physics 1: Problem Set 3
The Compton Effect and Spectral lines
1) A photon of initial energy 5.8  103 eV is deflected by 130 in a collision with a free electron,
which is initially at rest. What is the wavelength of the scattered photon? What energy (in eV) does
the electron acquire in the collision? What is the velocity of the recoil electron?
2) An electron and a photon have the same energy E= 25 keV. Compare the momenta of the two.
3) Calculate the percentage change in the wavelength of (i) an x-ray photon with wavelength
0.01nm and (ii) a ultraviolet photon with wavelength 500nm that undergo a 80 Compton scattering
from an electron?
4) Suppose a photon of initial wavelength 0.02nm undergoes two collisions with two electrons. In
the first collision, the photon is scattered through an angle of 80 and in the second collision
through an angle of 100. What is the final wavelength of the photon?
5) An incident x-ray photon of wavelength 0.0500nm is scattered in the backward direction (180o)
from a free electron that is initially at rest. Calculate the magnitude of the momentum of the
scattered photon. Calculate the speed of the electron after the collision.
6) A photon is emitted from a hydrogen atom that undergoes an electronic transition from the n = 5
state to the n = 2 state. Calculate (a) the energy, (b) the wavelength (in nm) and (c) the frequency of
the emitted photon?
7) Two of the wavelengths emitted in the hydrogen spectrum are 102.6nm and 1876nm. Calculate
the ni and nf values for each wavelength.
8) The energy levels of a hypothetical one electron atom is shown below. The potential energy is
taken to be zero when the electron is an infinite distance from the nucleus.
(a) Calculate the longest wavelength photon (in nm) which can just ionise the atom when the
electron is in the ground state.
(b) A 27eV photon is absorbed by the atom when it is in its ground state. When that atom returns to
its ground state, what possible energies can the emitted photons have? Include all possible
transitions.
(c) What will happen if a 14eV photon strikes the atom when it is in its ground state? Why?
_______________-3eV
_______________-6eV
_______________-15eV
_______________-30eV