Total number of $m$ values for $n = 4$ is

8

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16

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12

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20

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Solution

The correct option is D $16$
Total number of m values for n $=$ 4 is 16.
When $n = 44$ , $l = 0, 1,, . . . (n - 1) = 0, 1, 2, 3$ .
For $l = 0$ , $m = 0$
For $l = 1$ , $m = - 1, 0, + 1$
For $l = 2$ , $m = - 2, - 1, 0, + 1, + 2$
For $l = 3$ , $m = - 3, - 2, - 1, 0, + 1, + 2, + 3$
Total number of m values $= 1 + 3 + 5 + 7 = 16$
Note: For a given value of l, m can have values $- l, . . . . - 1, 0, + 1, . . . + l$

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