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  • State and discuss the Zeeman effect.
  • Define orbital magnetic field.
  • Define orbital angular momentum.
  • Define space quantization.

High-resolution measurements of atomic and molecular spectra show that the spectral lines are even more complex than they first appear. In this section, we will see that this complexity has yielded important new information about electrons and their orbits in atoms.

In order to explore the substructure of atoms (and knowing that magnetic fields affect moving charges), the Dutch physicist Hendrik Lorentz (1853–1930) suggested that his student Pieter Zeeman (1865–1943) study how spectra might be affected by magnetic fields. What they found became known as the Zeeman effect    , which involved spectral lines being split into two or more separate emission lines by an external magnetic field, as shown in [link] . For their discoveries, Zeeman and Lorentz shared the 1902 Nobel Prize in Physics.

Zeeman splitting is complex. Some lines split into three lines, some into five, and so on. But one general feature is that the amount the split lines are separated is proportional to the applied field strength, indicating an interaction with a moving charge. The splitting means that the quantized energy of an orbit is affected by an external magnetic field, causing the orbit to have several discrete energies instead of one. Even without an external magnetic field, very precise measurements showed that spectral lines are doublets (split into two), apparently by magnetic fields within the atom itself.

The figure shows the effect of magnetic field on spectral lines. In the first case, two spectral lines are shown when there is no external magnetic field. In the second case, when magnetic field is applied, the spectral lines split into several lines; the line on the left splits into three lines. The line on the right splits into five. In the third case, the magnetic field is large. The left line is again split into three lines and the right into five, but the split lines are farther apart than they are when the external magnetic field is not as strong.
The Zeeman effect is the splitting of spectral lines when a magnetic field is applied. The number of lines formed varies, but the spread is proportional to the strength of the applied field. (a) Two spectral lines with no external magnetic field. (b) The lines split when the field is applied. (c) The splitting is greater when a stronger field is applied.

Bohr’s theory of circular orbits is useful for visualizing how an electron’s orbit is affected by a magnetic field. The circular orbit forms a current loop, which creates a magnetic field of its own, B orb size 12{B rSub { size 8{"orb"} } } {} as seen in [link] . Note that the orbital magnetic field     B orb size 12{B rSub { size 8{"orb"} } } {} and the orbital angular momentum     L orb size 12{L rSub { size 8{"orb"} } } {} are along the same line. The external magnetic field and the orbital magnetic field interact; a torque is exerted to align them. A torque rotating a system through some angle does work so that there is energy associated with this interaction. Thus, orbits at different angles to the external magnetic field have different energies. What is remarkable is that the energies are quantized—the magnetic field splits the spectral lines into several discrete lines that have different energies. This means that only certain angles are allowed between the orbital angular momentum and the external field, as seen in [link] .

The figure shows an electron traveling in a circular orbit with radius r. A magnetic field B sub orb is oriented downwards and the orbital angular momentum L sub orb is oriented along the same line but upward, in a direction opposite B sub orb.
The approximate picture of an electron in a circular orbit illustrates how the current loop produces its own magnetic field, called B orb size 12{B rSub { size 8{"orb"} } } {} . It also shows how B orb size 12{B rSub { size 8{"orb"} } } {} is along the same line as the orbital angular momentum L orb size 12{L rSub { size 8{"orb"} } } {} .

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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