Question

The $KE$ of the electron in an orbit of radius $r$ in hydrogen atom is ($e$ = electronic charge)

• A. $\frac{e^{2}}{r^2}$
• B. $ \frac{e^{2}}{2r} $
• C. $ \frac{e^{2}}{r} $
• D. $ \frac{e^{2}}{2r^{2}} $

Answer 1

The Correct Option is B

$\frac{m v^{2} n}{r_{n}}=\frac{1}{4 \pi \varepsilon_{0}} \cdot\left(\frac{z e^{2}}{r^{2} n}\right)$ $=\frac{k z e^{2}}{r^{2} n} m v^{2}_{x}=\frac{Z e^{2}}{r_{v}}$ Kinetic energy of electron in $n$ an orbit $KE =\frac{1}{2} m v_{n}^{2}=\frac{k Z e^{2}}{2 r_{n}}$ $KE =\frac{e^{2}}{2 r}$