Q. Suppose an electron is attracted towards the origin by a force $\frac{k}{r}$ , where $k\ $is constant and $r$ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the $n$th orbital of the electron is found to be $r_{n}$ and the kinetic energy of the electron to be $T_{n}.$ Then which of the following is true?
A) $T_{n} \propto \frac{1}{n^{2}}\ ,\ r_{n} \propto \ n^{2}$
B) $T_{n}\ independent\ of\ n,\ r_{n} \propto \ n$
C) $T_{n} \propto \frac{1}{n},\ r_{n} \propto \ n$
D) $T_{n} \propto \frac{1}{n}\ ,\ r_{n} \propto \ n^{2}$
Explanation
(a) Radius of orbit
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ r_{n}$ $=$ $\frac{n^{2}h^{2}}{4\ \pi^{2\ }k^{2}m_{e}^{2}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ r_{n} \propto n^{2}$
Energy $E\ = \ - Rch\frac{Z^{2}}{n^{2}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ E \propto \frac{1}{n^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.