A factory uses a radioactive source and a detector to monitor the thickness of aluminium sheet as it is produced on a rolling mill. The aluminium sheet pass...

(a) Why beta is used rather than alpha [2]

Beta particles are partially absorbed by the aluminium sheet, so any change in the sheet's thickness produces a measurable change in the count rate reaching the detector. [1] Alpha particles would be completely absorbed by even a thin sheet of aluminium (their range in solid material is only a few micrometres), so none would reach the detector regardless of thickness. [1]

(b) Why gamma is also unsuitable [1]

Gamma rays are so penetrating that they would pass through the thin aluminium sheet with very little absorption. A change in thickness would produce almost no change in the count rate, making the measurement insensitive to thickness variations. [1]

(c) Why a long half-life is needed [1]

A long half-life ensures the activity of the source remains approximately constant over a long period, so the source does not need frequent replacement. This saves cost and reduces the number of times radioactive materials must be handled. [1]

(d) Activity after 10 years [3]

The half-life is 28 years and the source has been in use for 10 years.

Number of half-lives elapsed:

\(n = \frac{10}{28} = 0.357\) [1]

Using the exponential decay formula:

\(A = A_0 \times \left(\frac{1}{2}\right)^n = 6.0 \times \left(\frac{1}{2}\right)^{0.357}\)

\(= 6.0 \times 2^{-0.357} = 6.0 \times 0.781\) [1]

\(A = \mathbf{4.7 \text{ kBq}}\) (to 2 significant figures) [1]

Since 10 years is not a whole number of half-lives, the calculation uses the general formula \(A = A_0 \times (0.5)^{t/t_{1/2}}\) rather than the step-by-step halving method.