Question

An electron is in one of the $3d$-orbitals. What are the possible values of $n$, $l$ and $m$ for this electron?

• A. $n=3$, $l=0$, $m_l=0$
• B. $n=3$, $I=1$, $m_l=-1$, $0$, $+1$
• C. $n=3$, $l=2$, $m_l$, $-2$, $-1$, $0$, $+1$, $+2$
• D. $n=3$, $l=3$, $m_l=-3$, $-2$, $-1$, $0$, $+1$, $+2$, $+3$

Answer 1

Answer: (C)

For 3 rd-orbitals, principle quantum number, $n=3$
For $n^{\text{th }}$ orbital possible values of azimuthal quantum number, l are from o to $(n-1)$
Total of n values as $1=0,1,2$
Magnetic quantum number $m_1$ have values from $-1$ to $+1$ and total of $21+1$ values.
For $n=3$, possible values of 1 and $m_1$ are:
$m_1=-2,-1,0,1,2$ for $1=2$
$m_1=-1,0,1$ for $1=1$
$m_1=0$ for $1=0$