Teaching MPPSC Assistant Professor Mock Test Series 2025 Physical Sciences Atomic & Molecular Physics
In Stern - Gerlach experiment, a beam of silver atoms (each of mass m0) passes through a region of width Δx in direction of original beam. In this region a magnetic field gradient is setup along Z direction. Beam enters this region with speed 'v' and atoms get deflected by distance Δz when they leave this region. The magnetic field gradient \(\rm \frac{dB}{dz}\) is then given by {me is mass as electron ħ = h/2π}
1
\(\rm \frac{\mathrm{dB}}{\mathrm{dz}}=\frac{4 \mathrm{m}_{0} \mathrm{m}_{\mathrm{e}} \Delta \mathrm{z} v^{2}}{\mathrm{e\hbar}(\Delta \mathrm{x})^{2}}\)
2
\(\rm \frac{d B}{d z}=\frac{2 m_{0} m_{e} \Delta z v^{2}}{e \hbar(\Delta x)^{2}}\)
3
\(\rm \frac{d B}{d z}=\frac{m_{0} m_{e} \Delta z v^{2}}{2 e \hbar(\Delta x)^{2}}\)
4
\(\rm \frac{d B}{d z}=\frac{m_{0} m_{e} \Delta z v^{2}}{4 \mathrm{e\hbar}(\Delta x)^{2}}\)