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Nuclear Radius

Q2.

(a) Show that the kinetic energy of an α particle travelling at 2.00 × 107 ms–1 is 1.34 × 10–12J when relativistic effects are ignored.

'Relativistic effects' only happen when particles are travelling at very high speeds - near the speed of light. They are dealt with in the option papers - but not al papers - therefore they will always be ignored in questions like this.

Electron masses are not significant unless you are working to 5 significant figures

proton mass = 1.67 × 10-27 kg

electron mass = 9.11 × 10-31 = 0.000911 × 10-27 kg

m = 4 × 1.67 × 10–27 (kg)

m = 6.68 × 10–27 kg

kinetic energy = 1/2 mv2 = 0.5 × 6.68 × 10–27 × (2.00 × 107)2 = 1.34 × 10–12 J

(2 marks)

(b) Calculate the closest distance of approach for a head-on collision between the α particle referred to in part (a) and a gold nucleus for which the proton number is 79. Assume that the gold nucleus remains stationary during the collision.

loss in k.e. = gain in p.e.

1.34 × 10–12 = Q1Q2/(4πε0r) = 2e x 79e/(4πε0r) = 178e2/(4πε0r) = 178 x (1.60 × 10-19)2/(4πε0r)

r = 158 x (1.60 × 10-19)2/(4π x 8.85 × 10-12 x 1.34 × 10–12 )

r = 2.71 × 10–14 m

(4 marks)

(c) State one reason why methods other than α particle scattering are used to determine nuclear radii.

Any valid point such as:

    • strong force complicates the process
    • scattering caused by distribution of protons not whole nucleon distribution
    • alpha particles are massive causing recoil of nucleus which complicates results

(1 mark)

(Total 7 marks)