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)

half

Answer 2

de - Broglie wavelength is given by : $\lambda=\frac{h}{mv}\,...\left(i\right)$ $K.E.=\frac{1}{2}mv^{2}$ $v^{2}=\frac{2KE}{m}$ $v=\sqrt{\frac{2KE}{m}}$ 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 $1/2.$