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    The energy for absortion would be given by the energy difference of 2 fine energy levels.
    So delta_E = g_j * B_0 * mu_B * 1 = 9.26 E-5 eV

    Using the formula on slide 18.
    There are now 2 possible energy differences
    For the large one we can e.g. use m_j -3/2; m_i 1/2 to m_j -1/2; m_i 1/2
    We get an energy value of 1.89 E-7 eV for the first case
    and an energy value of 8.404 E-8 eV for the second case

    The first value will increase the overall energy value (it is higher than the previous splitting), while the second one goes between the previous 2 energy levels and therefore will lower the overal energy
    Or in other words, take the 9.26 E-5 eV, add the first value and substract the second one and we get: 9.27 E-5 eV

    For the lower energy value we need to (looking at the figure) do the exact opposite, therefore the new energy splitting is 9.2495 E-5 eV

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