In the Bohr's model of hydrogen-like atom the force between the nucleus and the electron is modified as F= e^2 4 ₀ ( 1 r^2 + r^3 ) , where is a constant. For this atom, the radius of the n^ th orbit in terms of the Bohr radius (a₀= ₀ h^2 m e^2 ) is :

Step-by-step solution

As F= m^2 r = e^2 4 ₀ ( 1 r^2 + B r^3 ) and mvr = nh 2 v = nh 2 mr m ( nh 2 mr )^2 1 r = e ^2 4 ₀ ( 1 r ^2 + B r ^3 ) or, 1 r ^2 + B r ^3 = mn ^2 ~h ^2 4 ₀ 4 ^2 ~m ^2 e ^2 r ^3 aligned & or, a ₀ n ^2 r ^3 = 1 r ^2 + B r ^3 & ( a ₀= ₀ ~h ^2 ~m e ^2 Given ) & r = a ₀ n ^2- B aligned