IB Physics HL E 1 9 Hl Closest Approach Questions

Calculate HL head-on scattering distances of closest approach by equating alpha-particle kinetic energy with electrostatic potential energy.

Exam points

derive and apply the head-on closest-approach relation by setting incident kinetic energy equal to Coulomb potential energy
calculate closest distance using alpha and nucleus charges, energy conversion from MeV to joules and consistent SI units
compare closest approach for different nuclear charges or incident energies and connect the result with scattering force and nuclear interaction range

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Study E.1.9 (HL)—Closest approach conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 2]

In an experiment, alpha particles of initial kinetic energy 5.9 MeV are directed at stationary nuclei of lead $\left({ }_{82}^{207} \mathrm{~Pb}\right)$ . Show that the distance of closest approach is about $4 \times 10^{-14} \mathrm{~m}$ .

2e AND 82e seen

OR

$3.2 \times 10^{-19}$ «C» AND $1.312 \times 10^{-17}$ «C» seen
$d=\frac{8.99 \times 10^{9} \times(2 e)(82 e)}{5.9 \times 10^{6} \times e}=3.998 \times 10^{-14} \approx 4 \times 10^{-14}<\mathrm{m} \gg$

Must see either clear substitutions or answer to at least 4 s.f. for MP2.

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IB Physics HL E 1 9 Hl Closest Approach Questions question 1