A beam of α-particles is incident on a thin gold foil. Most α-particles pass straight through the foil.
A few are deflected by gold nuclei.
The diagram shows the path of one α-particle which passes close to a gold nucleus N in the foil. The α-particle is deflected through an angle of 60° as it travels from A to B.
P marks its position of closest approach to the gold nucleus.
Another α-particle in the beam is deflected by the same gold nucleus N through an angle of 30°.
Sketch its path onto the diagram above.
The distance between P and N is 6.8 × 10–14 m.
Calculate the magnitude of the electrostatic force F between the α-particle (
) and the gold nucleus (
) when the α-particle is at P.
F = ......................................... N
The initial kinetic energy of each α-particle is 5.0 MeV.
Show that the magnitude of the initial momentum of each α-particle is about 10–19 kg m s–1.
Take the mass of the α-particle to be 6.6 × 10–27 kg.
The magnitude of the final momentum of the α-particle at B is equal to its initial value at A.
The gold nucleus N is initially at rest. During the passage of the α-particle from A to B, no other forces act on the two particles.
In the following questions label any relevant angles.
i) Draw two vectors in the spaces below to represent the initial momentum and the final momentum of the α-particle.
initial momentum at A
final momentum at B
[2]
ii) Draw a vector in the space below to represent the momentum of the nucleus N when the α-particle reaches B.
Explain how you determined this momentum.
[2]
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to determine g.