Question

An electron moving in $n=3$ orbit in hydrogen atom is at a distance of $1.28A$ from the nucleus. Calculate its velocity and wavelength.

Answer 1

Velocity of electron in any orbit is given as,

$V=\frac{2\pi e^{2}Z}{nh}=2.19\times {10}^6\frac{Z}{n}$

$V=2.19\times {10}^6\times \frac{1}{3}=0.73\times {10}^6$ m/s

We know that, $\frac{1}{\lambda }=\frac{C}{V}\Rightarrow \lambda =\frac{V}{C}$

$\lambda =\frac{0.73\times {10}^6}{3\times {10}^8}\Rightarrow 0.24\times {10}^{-2}M$

$\Rightarrow 2.4\times {10}^{-3}M$.