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)

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}} $