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Apply the binomial theorem (Appendix E)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 v is c/20, what is the value of (b) the classical exopression and (c ) the first-order correction? If the electron's speed is 0.85c, what is the value of (d) the classical expression and (e ) the first-order correction? (f) At what speed parameter beta does the first-order correction become 10% on greater of the classical expression? |
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