Question

A beam of spin-1/2 silver atoms travels along the +z-axis. The beam passes through a series of two Stern-Gerlach spin-analyzing magnets, each of which is designed to analyze the spin component along the y-axis. The first Stern-Gerlach analyzer allows only particles with spin up (along the y-axis) to pass through. The second Stern-Gerlach analyzer allows only particles with spin down (along the y-axis) to pass through. The particles travel at speed v between the two analyzers, which are separated by a region of length d in which there is a uniform magnetic field Bo pointing in the z-direction (just like the previous question, the results of which will prove essential here!) So, these particles are "in a uniform B field" for a fixed (given) time tₒ=d/v. Sketch the setup - convince yourself that this is the same situation as Q3. If Bₒ= 0, how many particles will be transmitted through the 2nd analyzer? Explain

Answer 1

If Bo = 0, no silver atoms will be transmitted through the second Stern-Gerlach analyzer, as the first analyzer already selected for spin up along the y-axis and no field is present to change their spins.

Step-by-step explanation:

The question is asking about a hypothetical experiment similar to the Stern-Gerlach experiment, which demonstrates the quantum mechanical property of spin. In this scenario, spin-1/2 silver atoms are first filtered by a Stern-Gerlach analyzer to allow only those with spin up along the y-axis to pass. These atoms then encounter a second analyzer that only allows atoms with spin down along the y-axis to pass. With a magnetic field of Bo = 0 in the z-direction, the atoms' spins would not be affected by the magnetic field as they travel from the first to the second analyzer, since there is no magnetic field to cause any transitions between spin states.

Therefore, if Bo = 0, none of the particles will be transmitted through the second analyzer. This is because all particles passing through the first analyzer have spin up along the y-axis, and there is no field to change their spin state before reaching the second analyzer that only permits spin down particles.