2025 DSS PRELIMS P1 Q13
2025 DSS PRELIMS P1 Q13
Secondary 4
6 marks
The mass, \(m\) mg, of a radioactive substance decreases with time, \(t\) hours. It is known that \(m\) and \(t\) are related by the equation \(m=Me^{-kt}\), where \(M\) and \(k\) are constants. The table below shows measured values of \(m\) and \(t\).
| \(t\) (hours) | 1 | 2 | 3 | 4 | 5 |
| \(m\) (mg) | 6.55 | 5.36 | 4.40 | 3.60 | 2.94 |
- Plot \(\ln m\) against \(t\) and draw a straight line graph.[2]
- Use your graph to estimate the initial mass of the substance,[2]
- the value of \(k\).[2]
Solution:
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Answer:(b) \(M=8.00\text{ mg}\) (c) \(k=0.200\text{ h}^{-1}\)
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