Question

An electron accelerated under a p.d. of V volt has a certain wavelength $\lambda$ . Mass of the proton is 2000 times the mass of an electron. If the proton has to have the same wavelength $\lambda$ , then it will have to be accelerated under p.d. of (volts):

• A. $100$
• B. $2000$
• C. $V/2000$
• D. $\sqrt{2000}$

Answer 1

The correct option is C $V/2000$

$\frac{1}{2}m{v}^2=eV$

$mv=\sqrt{2meV}$

$Now{\lambda }_e=\frac{h}{mv}$

$=\frac{h}{\sqrt{2meV}}$

${\lambda }_p=\frac{h}{\sqrt{2\times 2000m\times e\times V^1}}$

$Given,{\lambda }_e={\lambda }_p$

$V^1=\frac{V}{2000}$