In a Stern$-$Gerlach experiment, the deflecting force on the atom is $F_z=-{}_z(d\frac{B_z}{d}z),$ where ${}_z$ is given by equation ${}_z=-(2\mathrm{.}00232)\frac{e}{2m}*S_z$ and $d\frac{B_z}{d}z$ is the magnetic$-$field gradient. In a particular experiment the magnetic field region is $50\mathrm{.}0$ cm long; assume the magnetic$-$field gradient is constant in that region. A beam of silver atoms enters the magnetic field with a speed of $375\frac{m}{s}.$

Part A

What value of $d\frac{B_z}{d}z$ is required to give a separation of $1\mathrm{.}0$ mm between the two spin components as they exit the field? $($Note: The magnetic dipole moment of silver is the same as that for hydrogen, since its valence electron is in an $l=0$ state.$)$

Express your answer in teslas per meter.

$d\frac{B_z}{d}z=$

$\frac{T}{m}$