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Q.

An electron beam can undergo diffraction by crystals. Through the potential $10 \times x$ should a beam of electrons be accelerated so that its wave length becomes equal to 1.54 $A^{ο}$ . (Find the x value to the nearest integer)

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answer is 6.

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Detailed Solution

$\frac{1}{2} {mu}^{2} = eV; also λ= \frac{h}{mu}$

$\frac{1}{2} m \frac{h^{2}}{m^{2} λ^{2}} = eV or V= \frac{1}{2} \frac{h^{2}}{m λ^{2} e}$

$V= \frac{{(6.62 \times 10^{- 34})}^{2}}{2 \times 9.108 \times 10^{- 31} \times {(1.54 \times 10^{- 10})}^{2} \times 1.602 \times 10^{- 19}}$

$\begin{array}{l} 63.3 volt \\ 10 x = 63.3 \\ x = \frac{63.3}{10} = 6.33 \end{array}$

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An electron beam can undergo diffraction by crystals. Through the potential 10×x should a beam of electrons be accelerated so that its wave length becomes equal to 1.54 Aο . (Find the x value to the nearest integer)