The ratio of the energy of a photon emitted during the transition of an electron in a hydrogen atom from the level n=x to n=2 , to the energy of a photon emitted during the transition from n=4 to n=2 , is 28 25 . The value of x is

Step-by-step solution

The energy of a photon emitted during a transition from n₂ to n₁ in a hydrogen atom is given by: E = 13.6 ( 1 n₁^2 - 1 n₂^2 ) eV For the first transition ( n=x to n=2 ): E₁ = 13.6 ( 1 4 - 1 x^2 ) For the second transition ( n=4 to n=2 ): E₂ = 13.6 ( 1 4 - 1 16 ) = 13.6 ( 3 16 ) Given that the ratio E₁ E₂ = 28 25 : 1 4 - 1 x^2 3 16 = 28 25 1 4 - 1 x^2 = 28 25 3 16 1 4 - 1 x^2 = 7 25 3 4 = 21 100 1 x^2 = 1 4 - 21 100 = 25 100 - 21 100 = 4 100 1 x^2 = 1 25 x^2 = 25 x = 5 Answer: 5