how to distinguish between beta and gamma radiation with a Geiger-Mueller counter?

The Geiger counter is an instrument used for measuring ionizing radiation.It is widely used in such applications as radiation dosimetry, radiological protection, experimental physics and the nuclear industry.

Geiger counters are widely used to detect gamma radiation, and for this the windowless tube is used. However, efficiency is generally low due to the poor interaction of gamma rays compared with beta particles.High energy beta particles can also be detected by a thin-walled "windowless" G-M tube, which has no end window.

Put a a sheet of metal a few mm thick sheet in front of the detector.

If the count-rate is heavily reduced it is beta. (Beta can't pass through metal.)

If the count-rate is not reduced (or only slightly reduced) it is gamma, (Gamma can pass through thin metal.)