1. The problem statement, all variables and given/known data Determine the field gradient of a 50-cm-long Stern-Gerlach magnet (d1) that would produce a 1-mm separation at the detector between spin-up and spin-down silver atoms that are emitted from an oven at T=1500. Assume the detector is located 50 cm from the magnet (d2). Note: While the atoms in the oven have average kinetic energy 3kBT2, the more energetic atoms strike the hole in the oven more frequently. Thus the emitted atoms have average kinetic energy 2kBT2, where the kB is the Boltzmann constant. The magnetic dipole moment of the silver atom is due to the intrinsic spin of the single electron. The Bohr magneton, e[STRIKE]h[/STRIKE]/2mec≈5.788×10-9eV/G 2. Relevant equations Fz=μ⋅∂B/∂z≈μ∂Bz/∂z 3. The attempt at a solution The setup: the magnetic field gradient is oriented in the z-direction while the initial velocity of the atoms is in the x-direction. The separation between the silver atoms is 1-mm, therefore, the distance traveled in the z-direction by the silver atoms is 0.5 mm=5x10-2cm which I call dz. ∂Bz/∂z=∇B Fz=maz=μ∂Bz/∂z=μ∇B Average kinetic energy of the particles: 1/2mvx2=2kBT→vx=√(4kBT/m) vx=d1/t1→t1=d1/vx=d1√(m/4kBT) I know that while the atoms are in the field gradient they will be experiencing a force that causes them to move in the z-direction (I'm just sticking with the positive z-direction for simplicity) and once they're out of the field gradient they will be traveling at a constant velocity in both the x- and z-directions. I also know that I need to somehow relate all of this to the kinematic equations but I'm kind of at a loss right now. vz=azt1 (since there's no initial velocity in the z-direction and acceleration is constant).