Answer
(a) We can list the possible $3p$ states as $n, l, m$:
$n = 3, l = 1, m = -1$
$n = 3, l = 1, m = 0$
$n = 3, l = 1, m = 1$
(b) We can list the possible $3d$ states as $n, l, m$:
$n = 3, l = 2, m = -2$
$n = 3, l = 2, m = -1$
$n = 3, l = 2, m = 0$
$n = 3, l = 2, m = 1$
$n = 3, l = 2, m = 2$
Work Step by Step
(a) In the $3p$ state:
$n = 3$ and $l = 1$
$m = -1, 0 , 1$
We can list the possible $3p$ states as $n, l, m$:
$n = 3, l = 1, m = -1$
$n = 3, l = 1, m = 0$
$n = 3, l = 1, m = 1$
(b) In the $3d$ state:
$n = 3$ and $l = 2$
$m = -2, -1, 0 , 1, 2$
We can list the possible $3d$ states as $n, l, m$:
$n = 3, l = 2, m = -2$
$n = 3, l = 2, m = -1$
$n = 3, l = 2, m = 0$
$n = 3, l = 2, m = 1$
$n = 3, l = 2, m = 2$
