The ratio of the difference in energy between the first and the second Bohr orbit to that between the second and the third Bohr orbit is

Step-by-step solution

Energy of the ( n ^ th ) Bohr's orbit is given by (E_n=-13.6 z^2 n^2 e V ) For H -atom, ( Z =1 ) The difference in energy between the first and the second Bohr orbit: ( aligned & E₂-E₁=13.6 1^2 ( 1 1^2 - 1 2^2 ) & =13.6 3 4 e V aligned ) The difference in energy between the second and the third Bohr orbit: ( aligned & E₃-E₂=13.6 1^2 ( 1 2^2 - 1 3^2 ) & =13.6 5 36 e V aligned ) Taking the ratio, we get : ( E₂-E₁ E₃-E₂ = 13.6 3 4 13.6 5 36 = 27 5 )