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