IB Physics HL E 3 22 Hl Half Life and Decay Constant Questions

Derive and apply the HL relationship between half-life and decay constant to calculate decay times and remaining fractions.

Exam points

derive T_1/2=ln2/λ by substituting N=N0/2 into the exponential decay law
calculate elapsed time or remaining fraction from half-life, decay constant and the fraction decayed
identify which activity and sample quantities are required to determine half-life for a pure long-lived nuclide

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Study E.3.22 (HL)—Half-life and decay constant conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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This question is in two parts. Part 1 is about kinematics and gravitation. Part 2 is about radioactivity.

Part 1 Kinematics and gravitation

A ball is released near the surface of the Moon at time t=0. The point of release is on a straight line between the centre of Earth and the centre of the Moon. The graph below shows the variation with time t of the displacement s of the ball from the point of release.

Figure for Question IB Physics HL E 3 22 Hl Half Life and Decay Constant Questions question 1 — IB Physics HL

Calculate, in hour ${ }^{-1}$ , the decay constant of lead-212.

$\left.\quad \lambda=\frac{\ln 2}{\mathrm{~T}_{\frac{1}{2}}}=\frac{0.693}{10.6}=\right) 6.5 \times 10^{-2}$ hour $^{-1}$

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IB Physics HL E 3 22 Hl Half Life and Decay Constant Questions question 1