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Chapter 6: Q8DQ (page 1401)

In the ground state of the helium atom, one electron must have 鈥渟pin down鈥� and the other 鈥渟pin up.鈥� Why?

Short Answer

Expert verified

In order to satisfy Pauli's exclusion principle, since both electrons have the same quantum numbers (n, l,m1 ).

Step by step solution

01

Step 1:

In the helium atom, the two electrons are in the K-shell, so both have the principal quantum number n= 1

We know that the orbital quantum number can have values from 0 to n-1, so for n =1,=0 (only one possible value)

And the magnetic quantum number m can values from -lto +l; So, forl= 0,m1= 0 (also one possible value)

Thus, the two electrons have the same three quantum numbers, (n,l,m1).

So, in order for Pauli's exclusion principle to be satisfied, the fourth quantum number, the magnetic spin quantum numberms, must be different for the two electrons.

Since ms, can have only two values,ms=+12 spin up andms=-12 spin down, one electron of the helium atom must have spin up, and the other must-have spin down.

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