A beam of identical neutral particles with spin 1/2 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. Determine the smallest value of d such that 25% of the particles transmitted by the first analyzer are transmitted by the second analyzer.