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  4. The ratio of wavelengths of proton and deuteron accelerated through the same potential difference will be

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Q. The ratio of wavelengths of proton and deuteron accelerated through the same potential difference will be

Dual Nature of Radiation and Matter

Solution:

$\lambda=\frac{h}{\sqrt{2 q V m}}$
Since both proton and deuteron have same charge and accelerated through the same potential difference.
$\lambda \propto \frac{1}{\sqrt{m}} $
$\therefore \frac{\lambda_{p}}{\lambda_{d}}=\sqrt{\frac{m_{d}}{m_{p}}}$
$=\sqrt{\frac{2 m_{p}}{m_{p}}}=\sqrt{2}$