Question

The time of revolution of an electron around a nucleus of charge Ze in n^th Bohr orbit is directly proportional to ____________.

Options

• n

• `"n"^3/"Z"^2`

• `"n"^2/"Z"`

• `"Z"/"n"`

Answer 1

The time of revolution of an electron around a nucleus of charge Ze in n^th Bohr orbit is directly proportional to `"n"^3/"Z"^2`.

Explanation:

`"T" = (2pi"r")/"v"` ; radius of n^th orbit r_n `= ("n"^2 "h"^2)/(pi"mZe"^2,)`

speed of e^- in n^th orbit V_n `= ("Ze"^2)/(2epsilon "nh")`

`therefore "T" = (4epsilon_0^2  "n"^3 "h"^3)/("mZ"^2 "e"^4) Rightarrow "T" prop "n"^3 "Z"^2`