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

Step-by-step solution

The difference in energy between the first and second Bohr orbit is aligned & E₂-E₁=-13.6 z^2 ( 1 n₂^2 - 1 n₁^2 ) & =-13.6 (1)^2 ( 1 2^2 - 1 1^2 ) aligned =-13.6 (- 3 4 )=13.6 3 4 ...(i) The difference in energy between the second and third Bohr orbit is E₃-E₂=-13.6 z^2 ( 1 n₃^2 - 1 n₂^2 )=-13.6 (1)^2 ( 1 3^2 - 1 2^2 )=-13.6 ( -5 36 )=13.6 5 36 ...(ii) Ratio = E₂-E₁ E₃-E₂ = 3 4 5 36 = 3 4 36 5 = 27 5