Question

If the kinetic energy of an electron is increased four times, the wavelength of the de-Broglie wave associated with it would become

• A. one fourth
• B. half
• C. four times
• D. two times

Answer 1

Answer: (B)

de - Broglie wavelength is given by :
$\lambda =\frac{h}{mv}...\left(i\right)$
$K.E.=\frac{1}{2}m{v}^2$
$v^2=\frac{2KE}{m}$
$v=\sqrt{\frac{2KE}{m}}$
Substituting this in equation $\left(i\right)$
$\lambda =\frac{h}{mv}\sqrt{\frac{m}{2m\left(K.E\right)}}...\left(i\right)$
i.e. $\lambda \propto \frac{1}{\sqrt{KE}}$
$\therefore$ when $KE$ become 4 times wavelength become $1/2.$