The thickness t of an aluminium foil is to be determined using an experiment involving the absorption of β-particles. The sample of aluminium is placed between a β-source and a β-detector and the measured count rate varies according to the thickness of the aluminium foil as follows:

n = n₀ exp (-μt).

Given that the number n₀ of counts recorded in an interval of time in the absence of the foil is 572 and the number n of counts in the presence of the foil is 417, calculate the thickness of the foil and the error in this quantity μ is a constant with a value of (1.38+ 0.05) x 10³m^-1.

In a second experiment using a different technique the thickness, determined from five repeated measurements, is found to be 0.29 mm with a standard deviation of 0.1 mm. Comment upon whether the results of the two experiments are consistent.

For a material with a given value of μ. what thickness can be determined, using this radiation-counting technique, with the smallest percentage error?