Question

The energy that should be added to an electron to reduce its de Broglie wavelength from 1 nm to 0.5 nm is

• A. Four times the initial energy
• B. Equal to the initial energy
• C. Twice the initial energy
• D. Thrice the initial energy

Answer 1

The correct option is D Thrice the initial energy

$\lambda =\frac{h}{\sqrt{2mE}};\frac{{\lambda }^{\prime }}{\lambda }=\sqrt{\frac{E}{E^{\prime }}}\Rightarrow \frac{E}{E}={\left(\frac{0.5}{1}\right)}^2\Rightarrow E^{\prime }=\frac{E}{0.25}=4E$
The energy should be added to decrease wavelength. = E - E = 3E