Question

There are two electrons in the 1s orbital of the Helium atom. Write one complete sentence to explain how these two electrons can have different quantum numbers and thus obey the Pauli exclusion principle.

please show work

Answer 1

Helium - two electrons

First Electron

n = 1
ℓ = 0
m = 0
s = +1/2

The first electron in helium has exactly the same four quantum number of the first electron in hydrogen. However, helium has TWO electrons. So we "build up" from the previous electrons by adding one more.

Second Electron

n = 1
ℓ = 0
m = 0
s = -1/2

Notice the same n, ℓ, and m values, but s has shifted from positive 1/2 to negative 1/2. This was the problem Pauli saw in 1925. Three quantum numbers was insufficient to UNIQUELY identify each electron, but a fourth one (the one called s) did the trick.

Atomic Number	Element	n	ℓ	m	s	Orbital Name
2	Helium	1	0	0	+1/2	1s
		1	0	0	-1/2