Why is the Lande g-Factor for a Proton Different from That of an Electron?

[Amith2006]

Homework Statement

I know that the Lande g-factor for proton is 5.58 but I would like to derive it. Here, s=1/2, l=0 and hence j=1/2. But I don't get the required value. Moreover, we have an orbital and a spin g-factor for electrons but not for proton. Is it because protons are composite particles unlike electrons and hence more complex?

Homework Equations

g = 1 + {j(j+1) + s(s+1) – l(l+1)}/{2j(j+1)}

The Attempt at a Solution

 

[Jhero]

The Lande g-factor for a particle can be derived using the following equation:

g = 1 + (j(j+1) + s(s+1) – l(l+1))/(2j(j+1))

For a proton, s=1/2 and l=0, so j=1/2. Plugging in these values, we get:

g = 1 + (1/2(1/2+1) + 1/2(1/2+1) – 0(0+1))/(2*1/2(1/2+1))

= 1 + (3/4 + 3/4)/2 = 1 + (3/2)/2 = 1 + 3/4 = 5/4

This is not the same value as the Lande g-factor for a proton, which is 5.58. This could be due to the fact that protons are composite particles, made up of smaller particles called quarks. These quarks have their own intrinsic spin and angular momentum, which could contribute to the overall g-factor of the proton. Therefore, the Lande g-factor for a proton may not follow the same equation as for a single particle like an electron. More research and experiments would be needed to fully understand the g-factor of a proton.