Question

The force acting on the electrons in hydrogen atom (Bohr's theory) is related to the principle quantum number n as

Options

• n^-4

• n⁴

• n^-2

• n²

Answer 1

n^-4

Explanation:

The centripetal force provided by the electrostatic force causes the electron to move around the nucleus, which is given by

`"F"_"e"="Ze"^2/(4piepsilon_0"r"_n^2)=>"F"_"e"prop1/"r"_n^2`

Also, radius of orbit `"r"_n=(("h"^2epsilon_0)/(pi"me")) "n"^2/"Z"`

`=> "r"_nprop"n"^2`

From Eqs. (I) and (ii), we get

`"F"_eprop1/("n"^2)^2`

`=>"F"_eprop"n"^-4`