Question

The energy that should be added to an electron, to reduce its de-Broglie wavelengths from 10–10m to $0.5\times 10-10m,$ will be

• A. four times the initial energy
• B. thrice the initial energy
• C. equal to the initial energy
• D. twice the initial energy

Answer 1

The correct option is B thrice the initial energy

$\lambda =\frac{h}{\sqrt{2mE}}\Rightarrow \lambda \propto \frac{1}{\sqrt{E}}\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\sqrt{\frac{E_2}{E_1}}\Rightarrow \frac{{10}^{-10}}{0.5\times {10}^{-10}}=\sqrt{\frac{E_2}{E_1}}$
Hence added energy $=E_2-E_1=3E_1$