Chapter 1.15, Problem 27P

The velocity $\nu$ of electrons from a high energy accelerator is very near the velocity c of light. Given the voltage V Of the accelerator, we often want to calculate the ratio $\nu /c$.

The relativistic formula for this calculation is (approximately, for V >> 1)

$\frac{\nu }{c}=\sqrt{1-{\left(\frac{0.511}{V}\right)}^2}$, V = number of million volts.

Use two terms of the binomial series (13.5) to find $1-v/c$ in terms of V. Use your result to find $1-v/c$ for the following values Of V. Caution: V = the number 0f million volts.

(a) V = 100 million volts

(b) V = 500 million volts

(c) V = 25,000 million volts

(d) V = 100 gigavolts (100x10⁹ volts = 10⁵ million volts)