Advantages of Bohr's theory

(i) Bohr's theory satisfactorily explains the spectra of species having one electron, viz. hydrogen atom, He⁺, Li²⁺etc.

(ii) Calculation of radius of Bohr's orbit : According to Bohr, radius of  n^th orbit in which electron moves is

      Where, n = Orbit number, m = Mass number (9.1 * 10^-31 Kg), e = Charge on the electron (1.6 * 10^-19) z = Atomic number of element, k = Coulombic constant 9 * 10⁹Nm²c^-2

After we put the values of m,e,k,h, we obtain.

 

 (iii) Calculation of the velocity of an electron

(iv) Calculation of the energy of electron in the Bohr's orbit

Total energy of electron = K.E. + P.E. of electron 

Substituting of r, gives us    Where, n=1, 2, 3..........

Putting the value of m, e, k, h,∏ we obtain

When the electron jumps from the outer orbit (which is higher energy) n₂ to the inner orbit (which is lower energy) n₁ then the energy is emitted in the form of radiation which is given by

As we know that   and    

This can be represented as 

Where,   ; R is known as Rydberg constant. Hear the value to be used is 109678 cm^-1 

            The negative sign in above equations signifies that the electron and the nucleus form a bound system, which means that the electron is attracted towards the nucleus. Hence, if electron is to be taken away from nucleus, energy has to be supplied. The energy of the electron in n = 1 orbit is known the ground state energy; that in the n = 2 orbit is called the first excited state

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