vela said: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, mS=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.
The total spin quantum number, denoted by S, of a helium atom with 2 electrons in the first shell is 0. This is because each electron in the first shell has a spin quantum number of s = 1/2, and when combined, their spins cancel each other out resulting in a total spin of 0.
The total spin quantum number of a helium atom is determined by adding the individual spin quantum numbers of its electrons. Since helium has 2 electrons in the first shell, the total spin quantum number will be the sum of their spin quantum numbers, which is 1/2 + 1/2 = 1.
The total spin quantum number of a helium atom represents the total angular momentum of its electrons. It is also a quantum number that determines the spin state of the atom, which can affect its properties and behavior in certain situations.
No, the total spin quantum number of a helium atom cannot change as it is a quantum number that is constant for a given atom. However, the individual spin quantum numbers of its electrons can change if the atom undergoes a process such as ionization or electron excitation.
The total spin quantum number of a helium atom is unique to its configuration of 2 electrons in the first shell. Other atoms with different numbers of electrons will have different total spin quantum numbers, depending on the arrangement and number of electrons in their shells.