Practice portal › Atoms › Hydrogen Spectrum and Transitions

In a hydrogen-like atom, the radiation emitted due to the transition from n=4 to n=3 is found to be in the ultraviolet region. During which of the following transitions will the light emitted be in the infrared region?

Asked in RS Academy GUJCET booklet · Spectral series and wavelengths

Answer: (4) 5→4

Step-by-step solution

Idea: infrared photons carry less energy than ultraviolet ones, so the transition we want must release less energy than 4→3.

For a hydrogen-like atom the energy released is Δ E=13.6Z²(1/(n_f²)-1/(nᵢ²)) eV, so compare the brackets.

4→3: 1/9-1/(16)=7/(144)≈0.049.

2→1: 0.75; 3→2: 0.139; 4→2: 0.188 — all larger than 0.049, so all ultraviolet.

5→4: 1/(16)-1/(25)=9/(400)=0.0225, less than half the energy of 4→3.

Only 5→4 releases less energy than the ultraviolet line, so it is the transition that can give infrared light.

Why the other options are wrong

More Hydrogen Spectrum and Transitions questionsAll Hydrogen Spectrum and Transitions questions →

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.

Practise this with a timer