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Home » Crystal diffraction experiments can be performed using -rays, or electrons accelerated through appropriate voltage. Which probe has greater energy? (For quantitative comparison, take the wavelength of the probe equal to , which is of the order of interatomic spacing in the lattice)
Crystal diffraction experiments can be performed using X-rays, or electrons accelerated through appropriate voltage. Which probe has greater energy? (For quantitative comparison, take the wavelength of the probe equal to 1 \AA, which is of the order of interatomic spacing in the lattice) \left(m_{e}=9.11 \times 10^{-31} \mathrm{~kg}\right)
CBSE | Class 12 | Dual Nature of Radiation and Matter | NCERT | Physics
Crystal diffraction experiments can be performed using X-rays, or electrons accelerated through appropriate voltage. Which probe has greater energy? (For quantitative comparison, take the wavelength of the probe equal to 1 \AA, which is of the order of interatomic spacing in the lattice) \left(m_{e}=9.11 \times 10^{-31} \mathrm{~kg}\right)

For Electrons, we have the relation for kinetic energy as,
\mathrm{K} . \mathrm{E}=(1 / 2) \mathrm{m}_{\mathrm{e}} \mathrm{V}^{2}

=\left(\mathrm{m}_{\mathrm{e}} \mathrm{V}\right)^{2} / 2 \mathrm{~m}

\mathrm{K} . \mathrm{E}=\mathrm{p}^{2} / 2 \mathrm{~m}_{\mathrm{e}}

\Rightarrow p=\sqrt{2 m_{e} K \cdot E}

\lambda=\frac{h}{p}=\frac{h}{\sqrt{2 m_{c} K . E}}

\lambda^{2}=\frac{h^{2}}{2 m_{e} K \cdot E}

K \cdot E=\frac{h^{2}}{2 m_{e} \lambda^{2}}

K . E=\frac{\left(6.64 \times 10^{-34}\right)^{2}}{2 \times 9.1 \times 10^{-31} \times\left(10^{-10}\right)^{2}}

\mathrm{K} . \mathrm{E}=2.4 \times 10^{-17} \mathrm{~J}

\mathrm{K} . \mathrm{E}=\frac{2.4 \times 10^{-17}}{1.6 \times 10^{-19}}

=149.375 \mathrm{eV}

For photon of X-rays, the expression for energy is,
E=h c / \lambda e

=\left(6.63 \times 10^{-34} \times 3 \times 10^{8}\right) /\left(10^{-10} \times 1.6 \times 10^{-19}\right)

=12.375 \times 10^{3} \mathrm{eV}

=12.375 \mathrm{keV}

The energy of X-ray photons is greater than that of the electron.

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