An alpha particle is accelerated until its kinetic energy becomes 5.5 MeV.

Applied Nuclear Physics                                           Homework 6

Show your work. Include units.

1. An alpha particle is accelerated until its kinetic energy becomes 5.5 MeV.

(a)   Convert the energy of the alpha particle to joules.  (b)  What is the speed of the alpha particle after being accelerated?  (c)  What is the matter wavelength of the alpha particle at this speed?  The mass of an alpha particle is 6.68 x 10^-27 kg.

2. The speed of an electron is 1.40 x 10⁷ m/s. (a) What is the matter wavelength of the electron at this speed?  (b)  What is the radius of the smallest, stable circular motion that an electron moving at this speed can experience? (c) What is the radius of the second smallest circular motion?

3. The energy level diagram of singly ionized helium is shown below:

n =     E = 0

n = 4     E = -3.4 eV

n = 3     E = -6.04 eV

n = 2     E = -13.6 eV

n = 1     E = -54.4 eV

While in the N shell (n = 4 quantum state) the remaining electron makes a spontaneous transition to the M shell (n = 3 quantum state).  (a) How much energy does the electron lose in this transition?  (b) What is the wavelength of the photon emitted in this transition?  (c)  Where does this photon fall in the electromagnetic spectrum?  (d) Once in the n = 3 quantum state, how much energy must the electron absorb to become free of the atom?

4. While in the K shell (n = 1 quantum state) of the hydrogenic helium, the lone electron makes a bound-free transition when it absorbs a 115 angstrom unit photon. (a) What is the energy of the photon?  (b) What is the kinetic energy of the electron, once it leaves the atom?v