A source of monoenergetic alpha particles is directed at a particle detector through an absorber. We know the initially monoenergetic spectrum will demonstrate energy straggling, but the direction of the particles should not be altered and they should ALL make it to the detector, provided the thickness of the absorber is less than the thickness required to stop the slowest of the distribution. This is shown as the constant horizontal line in the graph at the bottom of the drawing. Once the absorber thickness is such that some of the slower particles are stopped, the width of the energy straggling curve presents itself in the slope of the fall-off from constant particle number detected down to zero. The mean range is the range at which the number of particles detected is one-half the original value.
Range is inversely proportional to the square of the charge of the charged particle.
The stopping power increases with increasing density. The range is inversely proportional to the density of the absorbing medium. The same statistical factors which account for energy straggling result in a straggling of range - the total path of energy depletion is different for each initially monoenergetic alpha. For protons or alphas, straggling results in a few percent variation about the mean range. The sharper the cut-off in the transmission, the less pronounced the range straggling.