some transition energies

homepage Forums EPR energy difference some transition energies

Viewing 1 post (of 1 total)
  • Author
    Posts
  • #3195 Score: 0
    Manon
    Participant

    1) Like we can see in the picture, the splitting due to the applied field will cause 4 new levels. Only transitions which obey the selection rules can happen (|\Delta m_J| = 1), and since the splitting between neighbouring levels are the same, only one frequency will be absorbed. This would be the one with energy g_J*µ_B*\|\Delta m_J|*B = 0.8*5.788(eV/T)*1*2T = 92,61 µeV.

    2) The levels are again splitted symmetrically around their original level, but now with an energy difference of A*m_I*m_J. The extra selection rule |\Delta m_I|=0 now also has to be satisfied. We will calculate following transitions (notation = (m_J, m_I):
    a) (-3/2, 1/2) to (-1/2, 1/2)
    b) (-3/2, -1/2) to (-1/2, -1/2)
    c) (-1/2, 1/2) to (1/2, 1/2)
    d) (-1/2, -1/2) to (1/2, -1/2)
    Because of the symmetrical splitting, we can already conclude that c and d will be the same.

    The energy levels have an energy E(m_I m_J) = -g_J*µ_B*m_J*B + A*m_I*m_J with A=g*\mu_N*B_hf/J. From this we can calculate the differences with ease:
    \DeltaE = -g_J*µ_B*B*(m_J-m_J’) + A*m_I*(m_J-m_J’)
    a) 46,25 µeV
    b) 46,35 µeV
    c=d) 92,56 µeV

Viewing 1 post (of 1 total)
  • You must be logged in to reply to this topic.