question_answer

Suppose an electron is attracted towards the origin by a force \[\frac{k}{r}\] where ‘k’ is a 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?                 [AIEEE 2008]

A) \[{{T}_{n}}\propto \frac{1}{n},\,{{r}_{n}}\propto n\]

B)      \[{{T}_{n}}\propto \frac{1}{n},\,{{r}_{n}}\propto {{n}^{2}}\]

C) \[{{T}_{n}}\propto \frac{1}{{{n}^{2}}},\,{{r}_{n}}\propto {{n}^{2}}\]       

D) \[{{T}_{n}}\] independent of \[n,\,{{r}_{n}}\propto n\]

Correct Answer: D

Solution :

[d]

Also,    which is independent of n.