Question

If the wavelength associated with a proton is $2.5\times {10}^{-13}\text{m}$, then determine the voltage through which it is accelerated.

• A. $10\text{kV}$
• B. $11\text{kV}$
• C. $12\text{kV}$
• D. $13\text{kV}$

Answer 1

The correct option is D $13\text{kV}$

Given:

$\lambda =2.5\times {10}^{-13}\text{m}$

The wavelength associated with a proton is given by,

$\lambda =\frac{0.286}{\sqrt{V}}\mathring{A}$

$\Rightarrow 2.5\times {10}^{-13}=\frac{0.286}{\sqrt{V}}\times {10}^{-10}$

$\Rightarrow V\approx 13\text{kV}$

Hence, option $\left(D\right)$ is the correct answer.