"Apply the binomial theorem (appendix E) to the last part ofeq K=mc^2(γ-1) for the kinetic energy of (an electron).
a) Retain the first two terms of the expansion to show thekinetic energy in the form K=(first term) + (second term). Thefirst term is the classical experession for kinetic energy. The second term is the first-order correction to the classicalexpression. ... (Use m for mass, v for velocity and c forthe speed of light.)"
The binomial theorem:
(1+x)^n = 1 + (nx/1!) + ((n(n-1)x^2)/2!) +...
I'm not sure if they mean just apply it to (γ-1) ormultiply through and apply it to (γmc^2-mc^2).
Parts b and d of this question ask:
If the speed is (c/22, .75c) what is the value of theclassical expression?
The classical expression for kinetic energy = (1/2)mv^2
For b and d I got the correct answers.
Parts c and e ask:
If its speed v is (c/22, .75c) what is the value of thefirst-order correction?
I'm not sure what the first-order correction is. I triedusing mc^2(γ-1) but that didn't work out.
Part f asks:
"In terms of c, at what speed v does the first-ordercorrection become 11% or greater of the classicalexpression?"