Q. According to Bohr’s theory of hydrogen atom, for the electron in the $n$th allowed orbit the (i) Linear momentum is proportional to 1/$n$ (ii)Radius is proportional to $n$ (iii)Kinetic energy is proportional to1/$\ n$$^{2}$ (iv) Angular momentum is proportional to $\ n$ Choose the correct option from the codes given below.
A) (i),(iii),(iv) are correct
B) (i) is correct
C) (i),(ii) are correct
D) (iii) is correct
Explanation
(a) According to Bohr’s theory of hydrogen atom , angular momentum is quantized $ie,$
$\ \ \ \ \ \ \ \ \ \ \ L\ = \ mv_{n}r_{n}\ = \ n\left( \frac{h}{2\pi} \right)$
Or L $\propto n$
Radius of the orbit $r_{n} \propto \frac{n^{2}}{Z}$
Kinetic Energy $= \frac{kZ^{2}e^{2}}{{2n}^{2}}$ $ie,$ $k$ $\propto \frac{1}{n^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.