As per given figure A, B and C are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavelengths ( i.e. λ₁/λ₂) is 7/(4 n), then the value of n will be __________.

Solution

Physics sir · 4 steps

First excited state means n = 2, not n = 1. Get the levels right and the ratio falls out.

1. Name the levels. The ground state is n = 1, so the first, second and third excited levels are n = 2, 3, 4. That makes A n = 2, B n = 3 and C n = 4. So λ₁ is the 3 → 2 jump and λ₂ is the 4 → 3 jump.

   1/λ = R(1/n_f²-1/nᵢ²)

2. Each wavelength. For λ₁: 1/λ₁ = R(1/4-1/9) = 5R/36. For λ₂: 1/λ₂ = R(1/9-1/16) = 7R/144.
3. Take the ratio. Wavelength is the inverse of 1/λ, so λ₁/λ₂ = (7R/144)/(5R/36) = (7 × 36)/(144 × 5) = 7/20.
4. So. Setting 7/20 = 7/4n gives 4n = 20, so n = 5.

The idea to keep. Excited levels are counted from the ground state: the k-th excited level is n = k + 1. For wavelength ratios, R cancels, so work with the brackets only and flip at the end.

Answer from the NTA final answer key. Solution by PrepWiser.