Apply the binomial theorem (Appendix E) to the last part of Eq. 37-52 for the kinetic energy of a particle.

(a) Retain the first two terms of the expansion to show the kinetic energy in the form K = (first term) + (second term). The first term is the classical expression for kinetic energy. The second term is the first-order correction to the classical expression. Assume the particle is an electron. If its speed y is c/20, what is the value of?

(b) The classical expression and

(c) The first order correction? If the electron's speed is 0.80c, what is the value of?

(d) The classical expression and

(e) The first-order correction?