Question

Calculate the accelerating potential that must be imparted to a proton is to give it an effective wavelength of $0.005nm$.

• A. $V=13.6volt$
• B. $V=32.82volt$
• C. $V=10.4volt$
• D. $V=1.23volt$

Answer 1

The correct option is B $V=32.82volt$

For proton, $u=\frac{h}{m\lambda }$
$\therefore u=\frac{6.626\times {10}^{-34}}{1.672\times {10}^{-27}\times 0.005\times {10}^{-9}}$
$=7.93\times {10}^4$ metre $se{c}^{-1}$ .....(i)
If accelerating potential is $V$, then velocity acquired by the changed particle having charge $Q$ and mass $m$,
$\left(1/2\right)m{u}^2=Q.V$
$u=\sqrt{\frac{2Q.V}{m}}=\sqrt{\frac{2\times 1.602\times {10}^{-19}}{1.672\times {10}^{-27}}\times V}$
By Eqs.(i) and (ii)
$V=32.82volt$