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 $1=0$