A student monitors the activity of a radioactive source Y with a Geiger counter

PHYSICS · Multi-part · A Level · Physics · Nuclear physics · Nuclear physics

Problem

A student monitors the activity A(t)A(t) of a radioactive source Y with a Geiger counter. A graph of A(t)A(t) versus time tt is provided verbally: • A=12,000 counts min−1A = 12{,}000\,\text{counts\,min}^{-1} at t=0 ht = 0\,\text{h} • A=6,000 counts min−1A = 6{,}000\,\text{counts\,min}^{-1} at t=6.0 ht = 6.0\,\text{h} • A=3,000 counts min−1A = 3{,}000\,\text{counts\,min}^{-1} at t=12.0 ht = 12.0\,\text{h} • A=1,500 counts min−1A = 1{,}500\,\text{counts\,min}^{-1} at t=18.0 ht = 18.0\,\text{h} would lie on the extension of the same smooth curve. Using only the information contained in this graphical description, respond to the following. (a) Determine the half-life of isotope Y from the graph. (b) Estimate the activity at t=18.0 ht = 18.0\,\text{h} if the trend continues. Justify your estimate based on the graphical pattern. (c) Using reasoning that relies exclusively on the plotted data, calculate the time at which the activity will first reach 750 counts min−1750\,\text{counts\,min}^{-1}. Explain each step in your reasoning.

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