Question

The Zeeman Effect is where spectral lines split into three in the presence of strong magnetic fields. The difference in energy can be expressed as ΔE = m_L μ_B B, where μ_B is the Bohr magneton (5.788 X 10^-5 eV/T) and B is the magnetic field in Tesla. What are the two extra colors (λ) that appear in a magnetic field of 5 T for the hydrogen alpha line (n = 3 to n = 2)?

Answer 1

The selection rule for Zeeman effect is ml = 1. Therefore, the difference in energy can be expressed as

The wavelength of emission line for a Hydrogen atom can be expressed as

Here, RH is the Rydberg constant = 1.0968 x 107 m-1. nf and ni are the final and the initial state of transition. In your problem the emission wavelength will be

Therefore, with the effect of magnetic field the line split into two other lines and they are

Corresponding wavelengths are