Question

what is the speed of an electron with kinetic energy 760 ev? express your answer to two significant figures and include the appropriate units. part b what is the speed of an electron with kinetic energy 0.48 kev? express your answer to two significant figures and include the appropriate units.

Explanation:

Step1: Convert energy to joules

The conversion factor is $1\ eV = 1.6\times10^{-19}\ J$. For part A, $K = 760\ eV=760\times1.6\times10^{-19}\ J = 1.216\times 10^{-16}\ J$. For part B, $K = 0.48\ keV=0.48\times10^{3}\times1.6\times10^{-19}\ J=7.68\times10^{-17}\ J$. The mass of an electron $m = 9.11\times10^{-31}\ kg$.

Step2: Use kinetic - energy formula

The kinetic - energy formula is $K=\frac{1}{2}mv^{2}$, so $v=\sqrt{\frac{2K}{m}}$.
For part A:
$v_A=\sqrt{\frac{2\times1.216\times 10^{-16}}{9.11\times10^{-31}}}\ m/s=\sqrt{\frac{2.432\times 10^{-16}}{9.11\times10^{-31}}}\ m/s\approx1.6\times 10^{7}\ m/s$.
For part B:
$v_B=\sqrt{\frac{2\times7.68\times 10^{-17}}{9.11\times10^{-31}}}\ m/s=\sqrt{\frac{1.536\times 10^{-16}}{9.11\times10^{-31}}}\ m/s\approx1.3\times 10^{7}\ m/s$.

Answer:

Part A:
$v = 1.6\times 10^{7}\ m/s$
Part B:
$v = 1.3\times 10^{7}\ m/s$