When solid caesium-137 decays by emitting a $\beta$-particle, solid barium-137 is produced, and this then emits a $\gamma$-ray. The barium-137 does not undergo any further decay. Caesium-137 has a half-life of 33 years. A pure block of caesium-137 has a mass of $2.0\,\mu\text{g}$. The diagram shows a radiation detector placed $5\,\text{cm}$ from the block. The detector gives a count rate of 2000 counts/second. Which statement is incorrect?
- AAfter 33 years, the mass of the block is $1.0\,\mu\text{g}$.
- BAfter 66 years, the sample contains $1.5\,\mu\text{g}$ of barium.
- CWith $5\,\text{cm}$ of lead between the block and the detector, the count rate is just above background level.
- DWith $2\,\text{mm}$ of aluminium between the block and the detector, the count rate is reduced significantly.