Task One

[pbutkiewicz5]

(Ia)
\hat{\mu}=\frac{g \mu_N}{\{hbar}}\hat{I}
expect value of \mu for eigenvalues of I in z dierction we have
\mu=\frac{g \mu_N}{\{hbar}}I, then
g=\frac{\mu}{\mu_N I}.
For Cd111 in ground state I=1/2, \mu=-0.5940 n.m., so
g=-0.5940/0.5=-1.188
For Cd111 in 245keV level I=5/2, \mu=-0.766 n.m., so
g=-0.766/2.5=-1.188=-0.3064
(Ib)
Magnetic moment \mu of an electron is related to its spin and the g-factor by the equation:
\mu=g\frac{e}{2m_e}S, we know that \mu_B=\frac{e\{hbar}}{2m_e}, so
\mu=g\frac{\mu_B}{2}(we substituted the equation for S=1/2{\hbar})
g=\frac{2\mu}{\mu_B} since we know that \mu=1\mu_B, we can rewrite
g=\frac{2\mu_B}{\mu_B}=2.
(Ic)
The magnetic moment of the neutron is
\mu=g\frac{\mu_N}{\{hbar}}S,
The angular momentów colerated with the spin of the proton S=1/2 is 1/2\{hbar}, so
\mu=g\frac{\mu_N}{2}, by substitution g=-3.826 we obtain
\mu=-1.913 n.m.

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