Question

How many electrons in an atom can share the quantum numbers n=2 l=1?

A) 1
B) 3
C) 6
D) 10

Answer 1

C) 6

Answer 2

l=1 can have px py and pz orbitals

Answer 3

px, py and pz can have 2 electrons each: 1 upspin and 1 downspin

Answer 4

There are 4 quantum numbers
-the principal quantum number (n) = integer in range 1 to infinity
-the angular quantum number (l) = integer in the range 0 to n-1
-the magnetic quantum number (m) = Ranges from -l to +l
-and the spin quantum number (s) = either -1/2 or +1/2

We write them as (n, l, m, s)
No we have n=2
l ranges from 0 to n-1, so thats 0 and 1
m ranges from -l to +l, that's -1, 0, and 1
s is either -1/2 or +1/2

Now we write them down (every pair has s -1/2 and +1/2
(2, 0, 0, +1/2)
(2, 0, 0, -1/2)

(2, 1, -1, +1/2)
(2, 1, -1, -1/2)

(2, 1, 0, +1/2)
(2, 1, 0, -1/2)

(2, 1, +1, +1/2)
(2, 1, +1, -1/2)

This means the atom can share 8 electrons

BUT, we have l=1 only here (since it's given in the question)
So we only pick those where l = 1

(n, l, m, s)
(2, 0, 0, +1/2)
(2, 0, 0, -1/2)

(2, \(\bbox[lime]{1}\), -1, +1/2)}
(2, \(\bbox[lime]{1}\), -1, -1/2)

(2, \(\bbox[lime]{1}\), 0, +1/2)
(2, \(\bbox[lime]{1}\), 0, -1/2)

(2, \(\bbox[lime]{1}\), +1, +1/2)
(2, \(\bbox[lime]{1}\), +1, -1/2)

So the answer is now 6 \(\large\ddot\smile\)