First of all, I know there are similar related questions but there is something that bothers me.
We can relate the magnetic moment and angular momentum as
$\vec{\mu} = \gamma \vec{l}$ (1)
So in the original experiment, if we don't think about spins (although we consider the orbitals of silver atoms which uses Pauli exclusion principle), silver atoms have zero orbital angular momentum and therefore the only contribution is the spin of the electron in the outermost shell, i.e. $(5s)^1$ electron. Doesn't this also mean that $\mu=0$, therefore, we should expect no deflection at all? But it is said that we should expect a continuous distribution of silver atoms due to their orientations.
In other words, $ F = \mu_z \frac{\partial B_z}{\partial z} = 0$ since $\mu_z = 0$