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In the hydrogen atom spectrum, λ 3 - 1 and λ 2 - 1 represent wavelengths emitted due to transition from second and first excited states to the ground state respectively. The ratio λ 3 - 1 λ 2 - 1 = p q , where p and q are the smallest positive integers. What is the value of p + q ?

Correct answer

59

Step-by-step solution

1 λ 3 - 1 = R 1 1 2 - 1 3 2 = 8 R 9 1 λ 2 - 1 = R 1 1 2 - 1 2 2 = 3 R 4 ⇒ λ 3 - 1 λ 2 - 1 = 27 32

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