The spin and magnetic moment (maximum z component) of in its ground state are and nuclear magnetons, respectively. A free nucleus is placed in a magnetic field of 2.16 T. We have to answer the following: (a) Into how many levels will the ground state split because of space quantization? (b) What is the energy difference between the adjacent pairs of levels? (c) In what region of the electromagnetic spectrum does this wavelength lie?

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The spin and magnetic moment (maximum z component) of in its ground state are and nuclear magnetons, respectively.

(a)

As the spin of nucleus, and it possesses magnetic moment, by space quantization the ground state will split in levels, when placed in a magnetic field.

(b)

The magnetic moment of is 3.26 . In a magnetic field B the ground state will split into four levels with energy difference

As , the energy difference between the levels will be

(c)

The wavelength of light corresponding to a photon of energy will be

The radiation will be in the TV FM range.