The Stern-Gerlach (S-G) experiment established that electrons have an intrinsic angular momentum, that is termed "spin". In the diagrams of S-G setups below, the source produces a beam of hydrogen atoms that propagates along the y-axis, but the spins of the hydrogen atoms can be along any direction. In the middle box the S-G axis indicates the direction of the nonuniform magnetic field, and a hashed box blocks the progress of a beam that was created by passing through the S-G instrument (indicated by a solid line, which does not continue past the hashed box). The third box represents a second S-G instrument, and the axis of its inhomogeneous magnetic field is indicated as either along the z or x axes. Note that the sources produce atoms with spins in all directions of space. (a) Following the notation used to indicate the spin states of the beams emerging from the first (left) S-G apparatuses below, indicate the spin states of the beams you expect to emerge from the second (right) S-G apparatus in each of the experiments below. (Note: z+ means the spin is toward the positive z direction). Briefly explain your answers.

The Stern-Gerlach (S-G) experiment established that electrons have an intrinsic angular momentum, that is termed "spin". In the diagrams of S-G setups below, the source produces a beam of hydrogen atoms that propagates along the y-axis, but the spins of the hydrogen atoms can be along any direction. In the middle box the S-G axis indicates the direction of the nonuniform magnetic field, and a hashed box blocks the progress of a beam that was created by passing through the S-G instrument (indicated by a solid line, which does not continue past the hashed box). The third box represents a second S-G instrument, and the axis of its inhomogeneous magnetic field is indicated as either along the z or x axes. Note that the sources produce atoms with spins in all directions of space. (a) Following the notation used to indicate the spin states of the beams emerging from the first (left) S-G apparatuses below, indicate the spin states of the beams you expect to emerge from the second (right) S-G apparatus in each of the experiments below. (Note: z+ means the spin is toward the positive z direction). Briefly explain your answers.