Question

An electron beam can undergo diffraction by crystals. if 63.573 m s${}^{-1}$ potential give a beam of electrons to be accelerated so that its
Wavelength becomes equal to:

• A. $1.2A^o$
• B. $1.54A^o$
• C. $2.2A^o$
• D. none of these

Answer 1

Answer: (B)

$1.54A^o$

For 1.54 A wavelength, the momentum for electron would be given by the expression
p = $\frac{h}{\lambda }$ $\Rightarrow$ v = $\frac{h}{m\lambda }$
The potential to which a beam of electrons be accelerated is given by the expression
eV = $\frac{1}{m{v}^2}$
i.e, V = $\frac{1}{2me}$($\frac{h}{\lambda }{)}^2$Substituting the values, we getV = $\frac{1}{\left(2\right)(9.1\times {10}^{-31}kg)(1.6\times {10}^{-19}C}$ ($\frac{6.626\times {10}^{-34}Js}{1.54\times {10}^{-10}m}{)}^2$
=63.573 m s${}^{-1}$