Calculate magnetic moment of carbon in first excitation state.

Carbon has atomic number is 6 and its electronic configuration is $1{\mathrm{s}}^{2}2{\mathrm{s}}^{2}2{\mathrm{p}}^2.$ At first excited state, one 2s electron excited and add to the last orbital of 2p and the configuration becomes $1{\mathrm{s}}^{2}2{\mathrm{s}}^{1}2{\mathrm{p}}^3.$

As there are four unpaired electrons, therefore the magnetic moment is calculated as:

$$\begin{gathered} \mathrm{\mu }=\sqrt{\mathrm{n}(\mathrm{n}+2)} \\ \mathrm{\mu }=\sqrt{4(4+2)}=4.89 \mathrm{BM} \end{gathered}$$