A beam of neutral hydrogen atoms with a speed of 104 m/s along the x-axis enters
ID: 1707771 • Letter: A
Question
A beam of neutral hydrogen atoms with a speed of 104 m/s along the x-axis enters a 1 m long region where there is an inhomogeneous magnetic field pointing in the z direction but with a gradient (variation) in the z direction given by .01 T/m. Given the atom's magnetic dipole moment of 9.27 x 10 -24 J/T, comput the following.a) the acceleration of the atoms while in the magnetic field region
b) the possible deflections in the z direction of the atoms as they pass through the magnetic field region, depending on whether the atom's magnetic moment is along the +z or -z direction.
Explanation / Answer
Given magnetic dipole momentum of hydrogen atomis _z = 9.27*10^ -24 J /T magnetic field pointing in the z direction but with a gradient (variation) in the z direction is dB / dz = 0.01 T /m Fotrce on neutral hydrogen atom is Fz = z ( dB / dz ) m a z = z ( dB / dz ) acceleration of the atoms while in the magnetic field region is az = z ( dB / dz ) / m here m is mass of hydrogen atom ( 1.67*10 6 -27 kg ) substitute the numerical value az = ( 9.27*10^ -24 ) ( 0.01 ) / ( 1.6*10 ^ -27 kg ) = 57.93 m/s ^2 b) the angular momentu of electron in z direction is L = m h _bar where m magnetic quantum number for hydrogen atom l = 0 m = ( l ( l +1 ) )1/2 = 0 So L _z = 0 Lcos = L _z = cos ^-1 ( 0) = 90 degrees = 0 So L _z = 0 Lcos = L _z = cos ^-1 ( 0) = 90 degreesRelated Questions
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