Question

No of subshelis having n = 4 & m = -2 are:

(1) 2
(2) 4
(3) 8
(4) 16

Answer 1

Shell with principal quantum number $n=4$ contains the subshells s, p, d and f.

Hence the possible azimuthal quantum numbers are,

$\longrightarrow l\in\{0,\ 1,\ 2,\ 3\}$

For s subshell, $l=0.$

For p subshell, $l=1.$

For d subshell, $l=2.$

For f subshell, $l=3.$

Or the possible values of azimuthal quantum number vary from 0 to $n-1.$

Value of magnetic quantum number m varies from -l to l.

For s subshell, $l=0$ and $m=0.$

For p subshell, $l=1$ and $m\in\{-1,\ 0,\ 1\}.$

For d subshell, $l=2$ and $m\in\{-2,\ -1,\ 0,\ 1,\ 2\}.$

For f subshell, $l=3$ and $m\in\{-3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3\}.$

We see only d and f subshells have $m=-2,$ i.e., 2 subshells.

Hence (1) is the answer.

Answer 2

• Given principal quantum number n=4 then the subshells are s, p, d and f.

Hence azimuthal quantum numbers are,

$\longrightarrow l\in\{0,\ 1,\ 2,\ 3\}$

• The values of azimuthal quantum number vary from 0 to n-1.

•Value of magnetic quantum number m varies from -l to l.

For s subshell, l=0 and m=0.

For p subshell, l=1 and $m\in\{-1,\ 0,\ 1\}..$

For d subshell, l=2 and $m\in\{-2,\ -1,\ 0,\ 1,\ 2\}..$

For f subshell, l=3 and$m\in\{-3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3\}.$

Observe that only d and f subshells have 2 subshells.

So, No of subshells = 2.

Hence Option (1) is the answer.

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HOPE IT HELPS :)