In hydrogen, A, B and C are the first, second and third excited levels respectively. The wavelengths λ₁ and λ₂ correspond to the transitions shown in the figure. If λ₁/λ₂ = 7/(4n), find n.

Question

G1 Physics · Accepted Answer

The first, second and third excited states of hydrogen are: A : n = 2 B : n = 3 C : n = 4 For transition 4 → 3, 1/λ₂ = R(1/3² - 1/4²) = R(1/9 - 1/16) = 7R/144 For transition 3 → 2, 1/λ₁ = R(1/2² - 1/3²) = R(1/4 - 1/9) = 5R/36 Therefore, λ₁/λ₂ = (7/144)/(5/36) = 7/20 Given, λ₁/λ₂ = 7/(4n) So, 7/20 = 7/(4n) 4n = 20 n = 5 Final answer: 5.