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 Plants constant $(h)$ is

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

Answer 1

Answer: (B)

$10\sqrt{h/m}$

Answer 2

Let the velocity of the particle $=v$
$\therefore$ Wavelength $(\lambda )$ of the particle
$=100\,v$ or $v=\frac{\lambda }{100}$
de-Broglie relationship is $\lambda =\frac{h}{m.v}$
$\lambda =\frac{h\times 100}{m.\lambda }$
or ${{\lambda }^{2}}=\frac{h\times 100}{m}$
$\lambda =10\sqrt{\frac{h}{m}}$