Question

An electron accelerated by a potential difference of V volt posses a de Broglie wave length . If the accelerating potential is increased by a factor of 4, the de-Broglie wavelength of the electron will be

• A. remains unchanged
• B. becomes double
• C. becomes half
• D. becomes 4 times

Answer 1

Answer: (C)

de-Broglie wavelength is given by $\lambda =\frac{h}{p}$
where, momentum of the particle $p=\sqrt{2mK}$
Kinetic energy of the particle $K=eV$
$⟹\lambda =\frac{h}{\sqrt{2meV}}$
We get $\lambda \propto \frac{1}{\sqrt{V}}$
Thus de-Broglie wavelength of the electron will become half if the accelerating potential is increased by a factor of $4$.