# Mass and Total Energy

Topics: Mass, Special relativity, Energy Pages: 2 (410 words) Published: December 22, 2012
1. There is an infinite non-multiplying medium with diffusion length 5 cm and diffusion coefficient 1 cm. In this medium there is an infinite plane source of neutrons on the x-y plane. Its strength is S1 = 1012 cm-2s-1. There is also a point source of strength S2=1012 s-1 located at z = 10 cm (above the plane source). Find the mathematical expressions and numerical values of the flux and current (magnitude and direction) at the midpoint between the point source and the plane source. Solution:

2. A point source of neutrons, of strength S = 108 cm-2s-1, is located at point (x1, y1, z1) = (-10 cm, 20 cm, 0). Calculate the neutron flux and current (magnitude and direction) at the point (x, y, z) = (50 cm, 40 cm, 0). As in Problem 1, take D = 1 cm and L = 5 cm. Solution:

Note: In the problems below, take c = 3.0*108 m.s-1.

3. Neutrons have a rest mass of 1.6749*10-27 kg (equivalent to 939.6 MeV). (a) A neutron has a total energy 945 MeV, what are its relativistic mass in MeV, its speed in m/s, its kinetic energy, and its momentum in kg.m.s-1? (b) Repeat the exercise for neutrons of total energy 960 MeV, 980 MeV, 1000 MeV Display all results in a Table.

Solution:

Total Energy (MeV)| Relativistic Mass (MeV)| Speed (m/s)| Kinetic Energy (MeV)| Momentum (kg.m.s-1)| 945| 945| 3.203*107| 5.4| 5.395*10-20|
960| 960| 6.150*107| 20.4| 1.053*10-19|
980| 980| 8.525*107| 40.4| 1.489*10-19|
1000| 1000| 1.027*108| 60.4| 1.830*10-19|

4. [Lamarsh p. 46 Problem 18 + a new part] An electron starting from rest is accelerated through a potential difference of 8 million volts. (a) What is its final kinetic energy?
(b) What is its total energy?
(c) What is its final mass?
(d) What is its speed, in m/s and as a fraction of c?
Solution:

5. [Lamarsh p. 47 Problem 25] An electron moves with a kinetic energy equal to its res-mass energy....