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 $\left(m\right)$ and Planck's constant $\left(h\right)$ 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

The correct option is B. $10\sqrt{\frac{h}{m}}$

The de-Broglie wavelength or a particle is given by,

$\lambda =\frac{h}{mv}$

According to given question $\lambda =100v$

$100v=\frac{h}{mv}$

so $v^2=\frac{h}{100m}$

$\lambda =100v$

$\lambda =10\sqrt{\frac{h}{m}}$

Hence, the correct option is $B$.