Q17. The first artificially produced isotope, phosphorus-30, was formed by bombarding an aluminium-27 isotope,with an α particle.

(a) Complete the following nuclear equation by identifying the missing particle.

(1 mark)

(b) For the reaction to take place the α particle must come within a distance, d, from the centre of the aluminium nucleus.

Calculate 'd' if the nuclear reaction occurs when the α particle is given an initial kinetic energy of at least 2.18 × 10–12 J.

The electrostatic potential energy between two point charges Q1 and Q2 is equal to:

where

r is the separation of the charges and

ε0 is the permittivity of free space.

The kinetic energy lost by the α particle approaching the nucleus is equal to potential energy gain.

Q1 = 2e (the charge on the alpha particle)

Q1 = 13e (the charge on the aluminium nucleus)

r = d

e = the magnitude of the charge on an electron = 1.6 x 10-19C

E = Q1Q2/4πε0r

2.18 × 10–12 = 13 x 2 (1.6 x 10-19)/4πε0d

d = 13 x 2 (1.6 x 10-19)/(4π x 8.85 x 10-12 x 2.18 × 10–12)

d = 2.75 x 10-15 m

(3 marks)

(Total 4 marks)