Question

An electron is in one of the 3D orbitals. Give the possible values of N, l and M for this electron.

Answer 1

Quantum numbers:-

• Quantum numbers are basically a set of numbers that define the position and energy of an electron in an atom.
• We know that:

Principal quantum number $\mathbf{n}$	Angular momentum quantum number $\mathbf{l}$	Magnetic quantum number ${\mathrm{m}}_{\mathrm{l}}$	Orbitals
$\mathrm{n}=1$	$0$	$0$	$1\mathrm{s}$
$\mathrm{n}=2$	$$\begin{gathered} 0 \\ 1 \end{gathered}$$	$$\begin{gathered} 0 \\ -1,0,1 \end{gathered}$$	$$\begin{gathered} 2\mathrm{s} \\ 2\mathrm{p} \end{gathered}$$
$\mathrm{n}=3$	$$\begin{gathered} 0 \\ 1 \\ 2 \end{gathered}$$	$$\begin{gathered} 0 \\ -1,0,1 \\ -2,-1,0,1,2 \end{gathered}$$	$$\begin{gathered} 3\mathrm{s} \\ 3\mathrm{p} \\ 3\mathrm{d} \end{gathered}$$

• According to the question, the electron is in $3\mathrm{d}$ orbital.
• This happens in the case where $\mathrm{n}=3$.
• And at $\mathrm{n}=3$, value of $\mathbf{l}$ is 2 and the value of ${\mathrm{m}}_{\mathrm{l}}$ as we can see from the table lies within $(-2\mathrm{to}2)$ that is $(-2,-1,0,1,2)$

Therefore, the possible value of $\mathbf{l}$ is 2, $\mathbf{n}$ is 3 and ${\mathrm{m}}_{\mathrm{l}}$ is $(-2,-1,0,1,2)$