Question

In the Zeeman effect, the energy levels of hydrogen are split by a magnetic field. Each state with a different value of mlml has a different energy. The differences in energy between adjacent values of mlml are all equal. The Zeeman effect is observed as a splitting in the spectral lines of hydrogen in the presence of a magnetic field. What is the greatest number of lines that a single spectral line can be split into by a magnetic field

Answer 1

Answer:

the Zeeman effect without spin is three lines

Explanation:

The Zeeman effect is the result of the interaction of the magnetic field with the orbital angular momentum of the electrons, if we do not take the spin into account it is called the Normal Zeeman effect.

Therefore we only take into account the orbital moments (m_l) of the transition, from the selection rules of the refreshed harmonics, only the transition with

             $\Delta m_l$ = 0, ± 1

            ΔE $\DeltaE = \mu_B \ \Delta m_l \ B$

Let's analyze for the case of the Hydrogen atom

For a transition between levels n = 1 and n = 2 the values ​​of m_l are n_f = 1 m_l = 0 and for n₀ = 2  m_l = 0, 1

so we only have two lines.

For transition n_f = 2 and n₀ = 3

n_f = 2    m_l = 0, 1

n₀ = 3      m_l = -1, 0, 1

There are only two lines plus the central line, so there are three spectral lines

for n_f = 3 and n_o = 4

n_f = 3   ml = -1, 0, 1

n₀= 4      ml = -2, -1, 0, 1, 2

Only transitions with  Δm_l = ±1 are allowed, so there are only two transitions plus the central transition (Δm_l = 0), so there are only 3 spectral lines.

In summary, due to the selection rule of spherical harmonics, the greatest number of lines in the Zeeman effect without spin is three lines.