i. What is de-Broglie wavelength of an electron moving with veloc… - Vidyadip

Question

i. What is de-Broglie wavelength of an electron moving with velocity of light? Mass of electron $=9.1 \times 10^{-31} \mathrm{~kg}$, $\mathrm{h}=6.626 \times 10^{-34} \mathrm{~J} \mathrm{~s}$.
ii. What is angular momentum of electron in the $5^{\text {th }}$ shell?

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Answer

$\text{m}=9.1\times10^{-31}\text{kg},$

$\text{c} =3.0\times10^8\text{ms}^{-1}$

$\lambda=\ ?,\text{h}=6.626\times10^{-34}\text{Js}$ or $\text{Kg}/\ \text{m}^2\text{s}^{-1}$

Applying de Broglie equation:

$\lambda=\frac{\text{h}}{\text{mc}}=\frac{6.626\times10^{-34}\text{kg/ m}^2\text{s}^{-1}}{9.1\times10^{-31}\text{kg}\times3.0\times10^8\text{ms}^{-1}}$

$\lambda=\frac{6.626}{27.3}\times10^{-34+31-8}\text{m}$

$\lambda=\frac{6.626}{27.3}\times10^{-11}=\frac{66.26}{27.3}\times10^{-12}\text{m}$

$\lambda=2.427\times10^{-12}\text{m}$

Angular momentum mvr $=\frac{\text{nh}}{2\pi}$

For $5^{\text {th }}$ energy level, $\text{n}=5$

$\therefore\text{mvr}=\frac{5\text{h}}{2\pi}$

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