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  4. The kinetic energy of an electron with de-Broglie wavelength of 0.3 nanometre is

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Q. The kinetic energy of an electron with de-Broglie wavelength of $0.3$ nanometre is

Dual Nature of Radiation and Matter

Solution:

$\lambda=\frac{h}{\sqrt{2 m E}}$
$\Rightarrow E=\frac{h^{2}}{2 m \lambda^{2}}$
$=\frac{\left(6.6 \times 10^{-34}\right)^{2}}{2 \times 9.1 \times 10^{-31} \times\left(0.3 \times 10^{-9}\right)^{2}}$
$=2.65 \times 10^{-18} J =16.8\, eV$