Edexcel A-Level Physics A2 4.4.98 Electric Potential in a Radial Field Questions

Practise Edexcel A-Level Physics radial electric potential by using point-charge formulas for nuclei, spheres and potential differences.

Exam points

use V equals kQ over r to calculate potential around point charges, nuclei or spheres
find closest approach by equating alpha-particle kinetic energy with electric potential energy
calculate potential difference or work done by summing potentials from two point charges

[Maximum number: 4]

In the early 20th century, experiments were carried out in which alpha particles were directed towards thin gold foil.

A simplified diagram of the apparatus used is shown.

Figure for Question Edexcel A-Level Physics A2 4.4.98 Electric Potential in a Radial Field Questions question 1 — Edexcel A-Level Physics A2

One experiment used gold foil made from the gold isotope ${ }_{79}^{197} \mathrm{Au}$ . The alpha particles had an initial kinetic energy of 4.7 MeV .

Show that the closest distance these alpha particles can get to a gold nucleus is about 5 x 10^-14 m.

Convert $4.7\,\mathrm{MeV}$ to $7.52\times10^{-13}\,\mathrm J$ , then equate this to the electrostatic potential energy: $7.52\times10^{-13}=\frac{(8.99\times10^9)(2e)(79e)}{r}.$ This gives $r=4.8\times10^{-14}\,\mathrm m$ , about $5\times10^{-14}\,\mathrm m$ .

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Edexcel A-Level Physics A2 4.4.98 Electric Potential in a Radial Field Questions question 1