Question

The ratio of (E2-E1) to (E4-E3) for the hydrogen atom is approximately equal to
(1) 10
(2) 15
(3) 17
(4) 12​

Answer 1

Answer:

15

Explanation:

Given The ratio of (E2-E1) to (E4-E3) for the hydrogen atom is approximately equal to

The energy of electron in nth orbit for hydrogen atom

     En = - 2π^2me^4 / n^2 h^2

Therefore E2 – E1 = - 2π^2me^4 / h^2[1/2^2 – 1/1^2]

                             = - 2π^2me^4 /  h^2 x 3/4

     Now E4 – E3 = - 2π^2me^4 /  h^2[1/4^2 – 1/3^2]

                            =  2π^2me^4 / h^2 x 7/144

So ratio of E2 – E1 / E4 – E3 will be

     = - 2π^2me^4 /  h^2 x 3/4 / 2π^2me^4 / h^2 x 7/144

    = 144 x 3 / 28

     = 15.42

    ≅ 15