Question

If the de-Broglie wavelength of a particle of mass $m$ is $100$ times its velocity then its value in terms of its mass $(m)$ and Planck's constant $(h)$ is

• A. $ \frac{1}{10}\sqrt{\frac{m}{h}} $
• B. $ 10\sqrt{\frac{h}{m}} $
• C. $ \frac{1}{10}\sqrt{\frac{h}{m}} $
• D. $ 10\sqrt{\frac{m}{h}} $

Answer 1

Answer: (B)

Let wavelength of particle be $x$.
Velocity, $v =\frac{x}{100}$
$\because \lambda =\frac{h}{m v}$
$\therefore x =\frac{h \times 100}{m \times x}$
$x^{2} =100 \frac{h}{m}$
$x =10 \sqrt{\frac{h}{m}}$