How do you calculate the strong isospin of nucleons?

[JustAnother]

First post, so hi everyone.

I have been banging my head against this question for a little while now. I've found two methods that appear to give the same result, but am not quite happy with what I've done:

Homework Statement

Calculate the strong isospin components of both tritium (3H) and helium-3 (3He)

Homework Equations

I've found two equations that give this value:

I_z = q/e - (S+B)/2

and

I_z = 1/2((n_up - n_antiup)- (n_down - n_antidown))

The Attempt at a Solution

Both of those give the result I_z = 3/2 for tritium and 1/2 for helium-3. However, the question tells me that both of them have total isospin I = 1/2. I was under the impression that I_z couldn't exceed I.

Am I wrong? Or have I got one of the calculations wrong?

EDIT: Oops- I think I see what I've done wrong. I assumed that 3H has 3 protons, when it obviously doesn't. Which makes me, well, an idiot.

 

[NateD]

The correct calculation should be Iz = 1/2((nup - nantiup)- (ndown - nantidown)) for both 3H and 3He, giving Iz = 1/2 for both.