For an electron in a $d$ orbital, the possible values of the magnetic quantum number $m_\ell$ range from $-\ell$ to $+\ell$, where $\ell$ is the azimuthal quantum number. For a $d$ orbital, $\ell = 2$.

Thus, the possible values of $m_\ell$ are:

$m_\ell = -2, -1, 0, +1, +2$

Expressed numerically, the possible values of $m_\ell$ for an electron in a $d$ orbital are:

$-2, -1, 0, 1, 2$.

Would you like further details or explanations? Here are some related questions you might consider:

1. What do the quantum numbers $n$, $\ell$, and $m_\ell$ represent?
2. How does the shape of the $d$ orbital compare to other orbitals?
3. What is the significance of the quantum number $\ell$?
4. Can you explain the distribution of electrons in orbitals?
5. How does the electron configuration change as you move across a period in the periodic table?

Tip: Remember that each orbital can hold a maximum of two electrons with opposite spins.