(C) The number of orbitals in a sub-shell is determined by the azimuthal quantum number,$\ell$. For a $d$ sub-shell,the value of $\ell$ is $2$. The nu

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(C) The number of orbitals in a sub-shell is determined by the azimuthal quantum number,$\ell$. For a $d$ sub-shell,the value of $\ell$ is $2$. The number of orbitals in a sub-shell is given by the formula $(2\ell + 1)$. Substituting $\ell = 2$ into the formula: $2(2) + 1 = 5$. Thus,there are $5$ orbitals in the $d$ sub-shell.