Question

For $\mathrm{l}=2$, how many orbitals are possible?

Answer 1

The number of orbitals:

• 'l' denotes azimuthal quantum number denoting the subshells, so for$\mathrm{l}=2$, the subshell denoted is 'd'.
• The number of orbitals corresponding to any subshell is given by the formula$(2\mathrm{l}+1)$.
• Hence, here the total number of orbitals possible for $\mathrm{l}=2$ (d subshell) is =$2\times 2+1=5$.
• Orbitals are denoted as the quantum number ‘m’, the value ranging from $+\mathrm{l}\mathrm{to}-\mathrm{l}.$
• So here for $\mathrm{l}=2$, the possible m values are, $-2,-1,0,+1,+2.$
• The orbitals corresponding to the value are ${\mathrm{d}}_{\mathrm{xy}},{\mathrm{d}}_{\mathrm{yz}},{\mathrm{d}}_{\mathrm{zx}},{\mathrm{d}}_{{\mathrm{x}}^2-{\mathrm{y}}^2}$ and ${\mathrm{d}}_{{\mathrm{z}}^2}$.

Hence, for l = 2, the number of orbitals possible are 5, given as ${\mathrm{d}}_{\mathrm{xy}},{\mathrm{d}}_{\mathrm{yz}},{\mathrm{d}}_{\mathrm{zx}},{\mathrm{d}}_{{\mathrm{x}}^2-{\mathrm{y}}^2}$ and ${\mathrm{d}}_{{\mathrm{z}}^2}$.