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You have set up an experiment where two Stern-Gerlach analyzers sequentially measure spin along the z-axis....

You have set up an experiment where two Stern-Gerlach analyzers sequentially measure spin along the z-axis. The first analyzer allows particles with spin up along z to pass. The second analyzer allows particles with spin down along z to pass. Between the two analyzers is a magnetic field aligned along +x. Your experiment sends identical spin-1/2 particles at speed v along the y-axis through the analyzers, which are separated by a distance Δy. What is the smallest distance Δy that will transmit 50% of the particles passed through the first analyzer through the second analyzer?

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