A-LevelPhysicsElectric fields9702/41 · May/June 2017 · Q57 Marks

An α-particle is travelling in a vacuum towards the centre of a gold nucleus, as illustrated in Fig. 5.1. [Figure 5.1] The gold nucleus has charge 79e. The gold nucleus and the α-particle may be assumed to behave as point charges. At a large distance from the gold nucleus, the α-particle has energy 7.7 × 10⁻¹³ J.

(a)The α-particle does not collide with the gold nucleus. Show that the radius of the gold nucleus must be less than 4.7 × 10⁻¹⁴ m.[3]
(b)Determine the acceleration of the α-particle for a separation of 4.7×10⁻¹⁴m between the centres of the gold nucleus and of the α-particle.[3]
(c)In an α-particle scattering experiment, the beam of α-particles is incident on a very thin gold foil. Suggest why the gold foil must be very thin.[1]

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Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[C1] (loss in) kinetic energy of α-particle = Qq / 4πε₀r
[M1] or 7.7 × 10⁻¹³ = Qq / 4πε₀r
[A1] 7.7 × 10⁻¹³ = 8.99 × 10⁹ × 79 × 2 × (1.60 × 10⁻¹⁹)² / r
[A1] r = 4.7 x 10⁻¹⁴ m
r is closest distance of approach so radius less than this
[C1] force = Qq / 4πε₀r² = ma
[C1] 8.99 × 10⁹ × 79 × 2 × (1.60 × 10⁻¹⁹)² / (4.7 × 10⁻¹⁴)² = 4 × 1.66 × 10⁻²⁷ × a
[A1] a = 2.5 x 10²⁷ m s⁻²
[B1] so that single interactions between nucleus and α-particle can be studied
[B1] or so that multiple deflections with nucleus do not occur

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