In a Stern - Gerlach experiment, a beam of hydrogen atoms in the ground state and with speed v = 600m / spass through a magnetic field gradient which applies a force on the electron moments. The field gradient is dB / d2 = 0.2T mm - 1, and the length of the field traversed is L = 12cm. Assuming that the atoms follow a classical trajectory and that the spin of the electron is along the + z direction, compute the acceleration of the atoms duo to the force on their electron moments, in the + z direction. Hint; using the expression for the energy U = mu B, compute first the force F2 = - dU / d2.
Explanation / Answer
The potential energy of the magnetic moments in the magnetic field is U = - B The force on the atom from the potential energy is F_z = - dU / dz = _z dB_z / dz = ( - e / 2 m ) L * - ( dB_z / dz ) acceleration is a = F / m = ( e / 2 m ) L ( dB_z / dz ) / m = ( 1.6*10^-19 C / 2 * 9.1*10^-31 kg ) * 12*10^-2 m ( 0.2 T *10^-3 /m ) / 9.1*10^-31 kg = 2.31*10^35 m/s^2