Question

The following quantum numbers are possible for how many orbital(s): $\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=+2$

• A. $4$
• B. $3$
• C. $1$
• D. $2$

Answer 1

The correct option is C

$1$

Explanation for the correct option

(c ) $1$

• $\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=+2$ denotes a $3\mathrm{d}$ orbital containing the magnetic quantum number $+2$.
• For $\mathrm{n}=3,\mathrm{l}=2$, we know that $\mathrm{m}=-2,-1,0,+1,+2$
• No two orbitals have the same magnetic quantum number.
• As a result, the provided quantum number is only achievable for one orbital and two electrons.
• Hence this option is correct.

Explanation for the incorrect options:

(a) $4$

• There are no two orbitals with the same quantum number.
• Hence no $4$ orbitals can have the same quantum numbers.
• This option is incorrect.

(b)$3$

• There are no two orbitals with the same quantum number.
• Hence no $3$ orbitals can have the same quantum numbers.
• This option is incorrect.

(d) $2$

• There are no two orbitals with the same quantum number.
• Hence no $2$ orbitals can have the same quantum numbers.
• This option is incorrect.

Hence the correct option is (C). The following quantum numbers are possible for one orbital.