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3. Atomic beam engineering A beam of spin ½ silver atoms travels along the +y-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 z-axis. The first Stern-Gerlach analyzer allows only particles with spin up (along the z-axis) to pass through. The second Stern- Gerlach analyzer allows only particles with spin down (along the z-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 $B_0$ pointing in the x- direction (just like the previous question, the results of which will prove essential here!) a) Sketch the setup. If $B_0$=0, how many particles will be transmitted through the 2nd analyzer? Explain. b) If $B_0$>0, find the smallest value of d such that 50% of the particles transmitted by the first analyzer are transmitted by the second analyzer. c) Very briefly, explain physically why particles are transmitted in part b (but not a)

          3. Atomic beam engineering
A beam of spin ½ silver atoms travels along the +y-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 z-axis. The first Stern-Gerlach analyzer allows
only particles with spin up (along the z-axis) to pass through. The second Stern-
Gerlach analyzer allows only particles with spin down (along the z-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 $B_0$ pointing in the x-
direction (just like the previous question, the results of which will prove essential here!)
a) Sketch the setup. If $B_0$=0, how many particles will be transmitted through the 2nd
analyzer? Explain.
b) If $B_0$>0, find the smallest value of d such that 50% of the particles transmitted by the
first analyzer are transmitted by the second analyzer.
c) Very briefly, explain physically why particles are transmitted in part b (but not a)

3. Atomic beam engineering
A beam of spin ½ silver atoms travels along the +y-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 z-axis. The first Stern-Gerlach analyzer allows
only particles with spin up (along the z-axis) to pass through. The second Stern-
Gerlach analyzer allows only particles with spin down (along the z-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 B0 pointing in the x-
direction (just like the previous question, the results of which will prove essential here!)
a) Sketch the setup. If B0=0, how many particles will be transmitted through the 2nd
analyzer? Explain.
b) If B0>0, find the smallest value of d such that 50% of the particles transmitted by the
first analyzer are transmitted by the second analyzer.
c) Very briefly, explain physically why particles are transmitted in part b (but not a)

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