Question

An atomic orbital has n = 3. What are the possible values of l and $m_l$ ?

List the quantum numbers ($m_l$ and l) of electrons for 3d orbital.

Which of the following orbitals are possible? 1p, 2s, 2p and 3f

Answer 1

n = 3 (Given)
For a given value of n, l can have values from 0 to (n – 1).
$\therefore$ For n = 3
l = 0, 1, 2
For a given value of l, $m_l$ can have ($2_l$ + 1) values.
For l = 0, m = 0 l = 1, m = – 1, 0, 1 l = 2, m = – 2, – 1, 0, 1, 2
$\therefore$ For n = 3
l = 0, 1, 2
$m_0$ = 0
$m_1$ = – 1, 0, 1
$m_2$ = – 2, – 1, 0, 1, 2

For 3d orbital, l = 2.
For a given value of l, ml can have (2l + 1) values i.e., 5 values.
$\therefore$ For l = 2 $m_2$ = – 2, – 1, 0, 1, 2

Among the given orbitals only 2s and 2p are possible. 1p and 3f cannot exist.
For p-orbital, l = 1. For a given value of n, l can have values from zero to (n – 1).
$\therefore$ For l is equal to 1, the minimum value of n is 2.
Similarly,
For f-orbital, l = 3.
For l = 3, the minimum value of n is 4.
Hence, 1p and 3f do not exist.