A beam of hydrogen atoms is used in a Stern-Gerlach type experiment. The atoms emerge from the oven with a velocity v = 104 m/sec. They enter a region 20 cm long where there is a magnetic field gradient fracdBdz = 3 times 104 T/m. The field gradient is perpendicular to the incident velocity of the a
A beam of hydrogen atoms is used in a Stern-Gerlach type experiment. The atoms emerge from the oven with a velocity $v = 10^4$ m/sec. They enter a region 20 cm long where there is a magnetic field gradient $\frac{dB}{dz} = 3 \times 10^4$ T/m. The field gradient is perpendicular to the incident velocity of the atoms. The mass of the hydrogen atom is $1.67 \times 10^{-27}$ kg. What is the separation of the two components of the beam as they emerge from the magnet? [5]
Quantity Value ------ Velocity $v = 10^4$ m/s Field region length $L = 0.20$ m Field gradient $dB/dz = 3 \times 10^4$ T/m Mass of H atom $m = 1.67 \times 10^{-27}$ kg Bohr magneton $\muB = 9.274 \times 10^{-24}$ J/T Force on each spin component: $F = \muB \dfrac{dB}{dz}$ (magnitude), directed opp...