Question

The energy that should be added to an electron to reduce its De broglie wavelength from ${10}^{-10}$ m to $0.5\times {10}^{-10}$ m will be :

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

Answer 1

The correct option is D Thrice the initial energy

As we know,

$\lambda =\frac{h}{\sqrt{2mE}}\Rightarrow \lambda \propto \frac{1}{\sqrt{E}}\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\sqrt{\frac{E_2}{E_1}}$
$\Rightarrow \frac{{10}^{-10}}{0.5\times {10}^{-10}}=\sqrt{\frac{E_2}{E_1}}\Rightarrow E_2=4E_1$
Hence added energy $=E_2-E_1=3E_1$