Question

An electron has total energy of $2MeV$. Calculate the effective mass of the electron in $Kg$ and its speed. Assume the rest mass of electron $0.511MeV$.

• A. $m_{eff}=23.6\times {10}^{-31}kg,u=3.9\times {10}^{10}cm$ $se{c}^{-1}$
• B. $m_{eff}=23.6\times {10}^{-19}kg,u=2.9\times {10}^{5}cm$ $se{c}^{-1}$
• C. $m_{eff}=2.16\times {10}^{-31}kg,u=1.9\times {10}^{10}cm$ $se{c}^{-1}$
• D. $m_{eff}=35.6\times {10}^{-31}kg,u=2.9\times {10}^{10}cm$ $se{c}^{-1}$

Answer 1

The correct option is D $m_{eff}=35.6\times {10}^{-31}kg,u=2.9\times {10}^{10}cm$ $se{c}^{-1}$

Effective mass $m_{eff}=\frac{9.1\times {10}^{-31}\times 2}{0.511}=35.61\times {10}^{-31}kg$

Mass of moving electron $=\frac{m_{rest}}{\sqrt{1-(\frac{u}{c}{)}^2}}$
$35.6\times {10}^{-31}=\frac{9.1\times {10}^{-31}}{\sqrt{1-(\frac{u}{3\times {10}^{10}}{)}^2}}$
$15.3=\frac{1}{1-(\frac{u}{3\times {10}^{10}}{)}^2}$
$0.065=1-(\frac{u}{3\times {10}^{10}}{)}^2$
$0.935=(\frac{u}{3\times {10}^{10}}{)}^2$
$u=2.9\times {10}^{10}$ cm/s