Q 12-11-020JEE MainAIEEE 2008Hard
Electrons accelerated through a potential difference $V$ are diffracted from a crystal whose planes are $d = 1$ Å apart. A strong diffraction peak is observed when the electrons are incident at an angle $i = 30°$ from the normal to the crystal planes, with the condition $2d\cos i = n\lambda$ ($n = 1$). $V$ should be about ($h = 6.6 \times 10^{-34}$ J s, $m = 9.1 \times 10^{-31}$ kg, $e = 1.6 \times 10^{-19}$ C)
Answer: (B) $50$ V
$\lambda = 2d\cos 30° = \sqrt{3}$ Å $\approx 1.73$ Å.
For an electron, $\lambda = \dfrac{12.27}{\sqrt{V}}$ Å, so $\sqrt{V} = \dfrac{12.27}{1.73} \approx 7.1$ and $V \approx 50$ V.
Solution by Sreeraj P, M.Sc Physics