Mathematical routines (MR)

Alpha decay of polonium-210

Unit 15
10 points
About 22 minutes

You can use a calculator on this question, just like on exam day.

A multipart problem where you use math to analyze a physical situation. You draw or sketch a representation such as a circuit diagram, a ray diagram or a graph, derive an equation using letters, calculate a numerical answer with units, and then make a claim or prediction and justify it with physics reasoning. On the exam: Question 1 of 4. New for May 2027: the free-response section is 95 minutes, down from 100, for all 4 questions (50% of your score), one of each type in this order. Calculator and equation sheet allowed. The CED suggests 20–25 minutes. This question type started in May 2025, so Physics 2 free-response questions from 2024 and earlier are built differently.

The question

Polonium-210, ${}^{210}_{84}\text{Po}$ , decays by alpha emission to an isotope of lead (Pb). Consider a polonium nucleus that is at rest when it decays. Atomic masses: polonium-210, 209.982874 u; lead-206, 205.974465 u; helium-4, 4.002603 u. Use 1 u = 931.5 MeV/c² = 1.66 × 10⁻²⁷ kg and 1 MeV = 1.60 × 10⁻¹³ J. The half-life of polonium-210 is 138 days.

Suggested time: 22 minutes

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Part (a)

2 points

Write the equation for this decay, including the nucleon number and atomic number of each particle, and explain how it satisfies the conservation laws for nuclear reactions.

Your answer to part (a)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

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Part (b)

2 points

(i) Describe the momenta of the lead nucleus and the alpha particle just after the decay. (ii) Derive an expression for the ratio $\frac{K_\alpha}{K_{\text{Pb}}}$ of their kinetic energies in terms of their masses $m_\alpha$ and $m_{\text{Pb}}$ .

Your answer to part (b)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

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Part (c)

3 points

Calculate (i) the decrease in mass in the decay, (ii) the energy released in the decay, and (iii) the kinetic energy of the alpha particle.

Your answer to part (c)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

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Part (d)

3 points

A sample contains 8.0 μg of polonium-210. (i) Calculate the mass of polonium-210 left after 414 days. (ii) A student claims that a polonium nucleus that has already existed for 138 days is more likely to decay during the next day than a polonium nucleus that formed recently, because it is “due” to decay. Do you agree or disagree? Justify your answer.

Your answer to part (d)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

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