Question

The kinetic energy of an electron get tripled then the de-Broglie wavelength associated with it changes by a factor

• A. $\frac{1}{3}$
• B. $\sqrt{3}$
• C. $\frac{1}{\sqrt{3}}$
• D. 3

Answer 1

Answer: (C)

$\frac{1}{\sqrt{3}}$

Answer 2

de-Broglie wavelength of an electron
$\lambda = \frac{h}{mv} = \frac{h}{\sqrt{2mK}}$
or $\lambda \propto \frac{1}{\sqrt{K}}$
$\therefore \frac{\lambda'}{\lambda} = \frac{1}{\sqrt{3K}} = \frac{\sqrt{K}}{1} = \frac{1}{\sqrt{3}}$
or $\lambda' = \frac{\lambda}{\sqrt{3}}$
Hence, de-Broglie wavelength will change by factor $\frac{1}{\sqrt{3}}$.