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Homework Help: Zeeman effect problem

  1. Apr 18, 2013 #1
    1. The problem statement, all variables and given/known data

    The red line of the Balmer series in hydrogen has a
    wavelength of 656.5 nm. Suppose that this line is observed to
    split into three different spectral lines when placed in a magnetic field, B, due to the Normal Zeeman Effect. What is the
    value of the magnetic field if the wavelength splitting between
    adjacent lines is 0.065 nm?

    2. Relevant equations

    [itex]\mu_{B}\ =\ 9.27400899(37)\ \times\ 10^{-24}\ J\ T^{-1}[/itex]

    [itex]E=E_0+\mu_B\times B\times m_l[/itex]

    3. The attempt at a solution

    I said that E - E0 = .065 nm

    and solved for B, saying m_l = 1, but that's not right.

    Any ideas?
  2. jcsd
  3. Apr 18, 2013 #2


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    Staff: Mentor

    E is an energy, nm is a length and not an energy. You can convert the wavelength values to energy values, then it will work.
  4. Apr 18, 2013 #3
    Ah right good catch. I tried that and got 3.3*10^8 T, but that was wrong too.

    i did [itex] E = \frac{hc}{\lambda}[/itex]

    where [itex]\lambda[/itex] is .065 nm

    than divided by [itex]\mu_B[/itex]
  5. Apr 18, 2013 #4


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    Homework Helper
    Gold Member
    2017 Award

    Note that ##E = \frac{hc}{\lambda}## does not imply that ##\Delta E = \frac{hc}{\Delta \lambda}##.
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