Atomic and Nuclear Physics Answers

Under certain conditions, a beam of electrons impinging on a crystal surface will diffract
and a scattering pattern of the beam can be obtained. What is the approximate kinetic
energy of the electrons needed in order to see the pattern?
(Assume the lattice spacing of the crystal to be 0.4nm )

A photon and an electron each have an energy of (6.0 X 10^3 eV). What are their
wavelengths? Which of these would you use to probe atomic structures?

238
92U decays spontaneously by α emission to 234
90Th. Calculate the total energy released by
this process and the recoil velocity of the 234
90Th nucleus. The atomic masses are 238.050783
u for 238
92U and 234.043595 u for 234
90Th.

Half life period of U234 is 2.5×105 years. In how many years it will remain 25% of original amount?

In a hydrogen atom, the proton and the electron are separated by an average distance 5 ∙ 10"## �. (a) Calculate the force that the proton exerts on the electron at this distance. (b) Calculate the electric field strength at the average location of the electron.

If a plane cuts the x, y and z axes at -4, 8 and -4 what is the Miller index of the plane?

In Section 5.2, the states of the vibrational model for even-2, even-N nuclei
up to the O+, 2+, 3+, 4+, 6+ three-phonon multiplet were discussed. The
model also gives selection rules for y emission: the phonon number must
change by exactly one unit, and only E2 transitions are permitted. Draw a
vibrational level scheme showing all permitted y transitions starting with
the three-phonon multiplet (use Figure 5.19 as a basis).

In Section 5.2, the states of the vibrational model for even-2, even-N nuclei
up to the O+, 2+, 3+, 4+, 6+ three-phonon multiplet were discussed. The
model also gives selection rules for y emission: the phonon number must
change by exactly one unit, and only E2 transitions are permitted. Draw a
vibrational level scheme showing all permitted y transitions starting with
the three-phonon multiplet (use Figure 5.19 as a basis).

(a) Pick half a dozen or so typical examples of 2+ + 0’ transitions from the
first excited states of “rotational” nuclei, 150 -= A < 190. (Use standard
reference works for nuclear spectroscopic data.) Compute the ratio between
the observed y decay rate and the corresponding Weisskopf estimate. Be
sure to correct the measured lifetimes for internal conversion if necessary.
(b) Repeat for “vibrational” nuclei, 60 < A < 150, excluding cases at
closed shells. (c) Draw any apparent conclusion about the difference between “rotational” and “ vibrational’’ y transitions.

An even-2, even-N nucleus has the following sequence of levels above its
Ot ground state: 2+ (89 keV), 4+ (288 keV), 6+ (585 keV), 0’ (1050 keV),
2+ (1129 keV). (a) Draw an energy level diagram and show all reasonably
probable y transitions and their dominant multipole assignments. (b) By
considering also internal conversion, what additional transitions and multipoles would appear?