Question

Bohr Formule.

Answer 1

Let the charge of atomic nucleus be Ze (for hydrogen z = 1). When the electron is moving in an orbit of radius r_n , the centripetal force maintaining it in this orbit is coulomb electrostatic force

Multiplyaing both sides of this equation by r\(^2_n\).

Squarring Bohr’s condition of Ist postutate we have

Comparing above two equations we have

To calculate the energy of the electron in n^th permitted orbit we notice that this energy will comprise the potential as well kinetic energy of the electron.

Hence the energy of the electron in the n^th orbit is

Using Bohr’s second postulate we can write

Putting the value of constants we get the value of R as 1.099 x 10⁷ m^-1 

The experimental determined value of R from spectroscopic measurement is 1.097 x 10⁷ which remarkably well agrees with the value of R obtained on the basis of Bohr’s posulates.