The ratio of the difference in energy between first and second Bohr orbit

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

Options

(a) 1/2
(b) 1/3
(c) 4/9
(d) 27/5

Correct Answer:

27/5

Explanation:

E₁ – E₂ = 1312 x Z²(1/1² – 1/2²)
= 1312 x Z²(3/4)
E₂ – E₃ = 1312 x Z²(1/2² – 1/3²)
= 1312 x Z²(5/36)
From eqs. (i) and (ii)
E₁ – E₂ / E₂ – E₃ = 3 x 26 / 4 x 5 = 27/5

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