A beam of spin-21 particles with speed v0 passes through a series of two SGz devices. The first SGz device transmits particles with Sz=ℏ/2 and filters out particles with Sz=−ℏ/2. The second SGz device transmits particles with Sz=−ℏ/2 and filters out particles with Sz=ℏ/2. Between the two devices is a region of length l0 in which there is a uniform magnetic field B0 pointing in the x direction. Determine the smallest value of l0 such that exactly 25 percent of the particles transmitted by the first SGz device are transmitted by the second device. Express your result in terms of ω0=egB0/2mc and v0.