Question

If the de-Broglie wavelength is l₀ for protons accelerated through 100V, that for alpha particles accelerated through the same voltage will be –

• A. l₀
• B. l₀/2
• C. $\frac{\lambda_{0}}{2\sqrt{2}}$
• D. None of these

Answer 1

Answer: (C)

$\frac{\lambda_{0}}{2\sqrt{2}}$

Answer 2

l₀ =$\frac{h}{\sqrt{2(m_{p})eV_{0}}}$

l' =$\frac{h}{\sqrt{2(4m_{p})(2e)V_{0}}}$

$\frac{\lambda_{0}}{\lambda'} = \sqrt{8} = 2\sqrt{2}$

l' =$\frac{\lambda_{0}}{2\sqrt{2}}$