A beam of particles, each of mass m and (nonrelativistic) speed v, strikes a barrier in which there are two narrow slits and beyond which is a bank of identical detectors. The two slits may be of different widths and thus permit particles to pass through at two different probabilities. The "center" of the detector bank is the one equidistant from both slits. With slit 1 alone open, 100 particles per second are counted by each detector. Now slit 2 is also opened. An interference pattern is noted in which the first minimum, 36 particles per second, is observed by a detector positioned at an angle of 30 from the initial direction of incidence of the beam. (a) How far apart are the two slits? State your result in terms of h, m and v. (b) How many particles per second would be counted (by any one of the detectors) when only slit 2 alone is open? There are multiple answers: state all of them!