Total spin quantum number of helium atom with 2 electrons in first shell

[umagongdi]

Homework Statement

A helium atom had two electrons in the first shell (1s). Explain, withour detailed derivation, what the value of the total spin quantum number is.

Homework Equations

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The Attempt at a Solution

Since the 2 electrons are in the first (1s) shell they must have opposite spins, +1/2, and -1/2 due to pauli exclusion principle. The total spin must be their sum +1/2-1/2=0. Therefore the atom spin is 0? Can atoms have spin 0?

 

[vela]

A couple of misconceptions:

1) That's not the spin of the atom. The spin of the atom is the sum of the electronic spin, the nuclear spin, and the orbital angular momentum. (There's no reason the spin of an atom can't be 0.)

2) You've shown that the z-component of the total electronic spin is 0. You haven't shown that the total spin is 0. It's possible, for instance, that the electrons are in the S=1, m_S=0 state.

I'm guessing the problem isn't asking about the atom's spin but just the total electronic spin. When you have two spin-1/2 particles, their spins can combine to form an S=0 or S=1 state. You need to explain why one of them is not allowed.

 

[umagongdi]

A couple of misconceptions:

1) That's not the spin of the atom. The spin of the atom is the sum of the electronic spin, the nuclear spin, and the orbital angular momentum. (There's no reason the spin of an atom can't be 0.)

2) You've shown that the z-component of the total electronic spin is 0. You haven't shown that the total spin is 0. It's possible, for instance, that the electrons are in the S=1, m_S=0 state.

I'm guessing the problem isn't asking about the atom's spin but just the total electronic spin. When you have two spin-1/2 particles, their spins can combine to form an S=0 or S=1 state. You need to explain why one of them is not allowed.

I asked the proffesor and he said the same, that the answer was just for the z-axis, he didn't explain. Why is this for the z-axis? Is the total spin just the sum of all the spins? But we don't know the nuclear spin etc?

 

[vela]

You need to go back and review the addition of angular momentum in quantum mechanics. This is a fundamental topic in quantum mechanics that you need to know. In particular, you should be able to apply the concepts to two spin-1/2 particles to find their total angular momentum.

 

[umagongdi]

thanks