A set of axes shows a smooth, monotonically decreasing curve for the number of undecayed nuclei N(t) of a pure radioactive isotope X.
• At t=0min the curve passes through N=8000.
• At t=4.0min it passes through N=4000.
• At t=8.0min it passes through N=2000.
Subsequent points continue the same pattern, producing a characteristic decay shape.
Answer the following in the context of this graph.
(a) Determine the numerical value of the half-life of isotope X, including appropriate units, using only the information provided by the graph.
(b) Describe, with reference to specific features of the plotted data, why the shape of the curve is consistent with exponential decay rather than linear or quadratic decline.