Physics 251 Spring 1999
Modern Physics
Homework Assignment # 4, Due (in class) Monday February 15

Reading Ahead: Read Krane, Chapter 5, week of Feb. 7 Problem Assignment: Important! There are three formulas for kinetic energy:

$$\frac{1}{2}mv^2=\frac{p^2}{2m}$$ Eq.(1.1) KE = usual classical formula

$$\sqrt{(mc^2)^2 +(pc)^2}-mc^2$$ Eq.(2.36) KE = Einstein formula; general

Eq.(2.42) KE = pc extreme relativistic or massless case

Case A is an approximation which is accurate when v is small compared with c or equivalently when KE is small compared with mc², which is very often accurate. In each of the problems below you must specify which (A,B,C) of these three formulas is appropriate. It is significant that in all three cases the velocity v is given by dE/dp. In case B this is equivalent to the formula $p=mv/\sqrt{1-(v/c)^2}.$

1.

Krane, Chapter 4, p.132, #1. Reminder: according to elementary kinetic theory, the average kinetic energy of a particle of mass m in thermal equilibrium is 3k_B T/2.

2.

Krane, Chapter 4, p.132, #2.

3.

Krane, Chapter 4, p.132, #3. Reminder: the optimal spatial resolution is approximately the same as the wavelength of the wave used to image the object.

4.

Krane, Chapter 4, p.133, #11. Refer to fig. 4.6 and use it to derive the formula $d \sin \phi=n \lambda$.

5.

Krane, Chapter 4, p.133, #15.

6.

Krane, Chapter 4, p.133, #17.

7.

Krane, Chapter 4, p.134, #26.