Q147 / 150 · MHT CET 2021 (20 Sep Shift 1) · Physics

What is the additional energy that should be supplied to a moving electron to reduce its de Broglie wavelength from $1 \mathrm{~nm}$ to $0.5 \mathrm{~nm}$ ?

A
Four times its initial energy
B
Five times its initial energy
C
Two times its initial energy
Correct answer
D
Three times its initial energy

Solution

De Broglie wavelength, $\lambda=\frac{\mathrm{h}}{\mathrm{mv}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}$ $$ \Rightarrow \mathrm{E}=\frac{\mathrm{h}^2}{2 \mathrm{~m} \lambda^2} $$ If $\lambda$ is halved, then kinetic energy becomes 4 times or increased by three times.

Hence, the correct answer is option: 'D'.

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