An electron moving with velocity $1.6 \times 10^7 \mathrm{~m} / \mathrm{s}$ has wavelength of $0.4 Å$. The…
An electron moving with velocity $1.6 \times 10^7 \mathrm{~m} / \mathrm{s}$ has wavelength of $0.4 Å$. The required accelerating voltage for the electron motion is [charge on electron $=1.6 \times 10^{-19} \mathrm{C}$, mass of electron $\left.=9 \times 10^{-31} \mathrm{~kg}\right]$
$7.2 \times 10^3 \mathrm{~V}$
$7.2 \times 10^2 \mathrm{~V}$
$7.2 \mathrm{~V}$
$7.2 \times 10^{-2} \mathrm{~V}$
Solution
When an electron is accelerated through a voltage its kinetic energy is converted into electric potential energy:
$\begin{aligned}
\mathrm{K} & =\mathrm{U} \\
& \frac{1}{2} \mathrm{mv}^2=\mathrm{eV} \\
\therefore \quad \mathrm{V} & =\frac{\mathrm{mv}^2}{2 \mathrm{e}} \\
& \mathrm{V}=\frac{\left(9 \times 10^{-31}\right)\left(1.6 \times 10^7\right)^2}{2 \times 1.6 \times 10^{-19}}=7.2 \times 10^2 \mathrm{~V}
\end{aligned}$