Nuclear Radius


(a) Scattering experiments are used to investigate the nuclei of gold atoms.

In one experiment, alpha particles, all of the same energy (monoenergetic), are incident on a foil made from a single isotope of gold.

(i) State the main interaction when an alpha particle is scattered by a gold nucleus.

The electromagnetic (or electrostatic or Coulomb) interaction

[1 mark]

(ii) The gold foil is replaced with another foil of the same size made from a mixture of isotopes of gold. Nothing else in the experiment is changed.

Explain whether or not the scattering distribution of the monoenergetic alpha particles remains the same.

The mark requires a described distribution and the reason for it.

The scattering distribution remains the same because the alpha particles interact with a nucleus whose charge/proton number/atomic number remains the same and therefore the repulsive force remains the same.

The scattering distribution will change - it will become less distinct because there is a mixture of nuclear masses (which gives a mixture of nuclear recoils).

The reference must be made to the mass variation and not density or size variation for the mark to be awarded.

[1 mark]

(b) Data from alpha-particle scattering experiments using elements other than gold allow scientists to relate the radius R, of a nucleus, to its nucleon number, A.

The graph below shows the relationship from the data obtained from a scattering experiment. The data obtained obeys the relationship R = r0 A1/3

(i) Use information from the graph to show that r0 is about 1.4 × 10–15 m.

Any point on the line can be used to obtain corresponding values of R and A - they can then be inserted into the equation to calculate r0. The simplest is to read off the value for A = 175

r0 = 8.0 x 10-15 / 1751/3

r0 = 1.43 x 10-15 m

The substitution and calculation must be shown for the mark.

[1 mark]

(ii) Show that the radius of a nucleus is about 5 × 10–15 m.

R = r0 A1/3

R = 1.43 x 10-15 x 511/3

R = 5.3 x 10-15 m

(R = 5.2 x 10-15 m from r0 = 1.4 x 10-15 m)

The first mark was awarded for putting the correct value for A into the equation, the second mark was for calculating the value to compare to the given one which must be 2 or more significant figures.

[2 marks]

(c) Calculate the density of a nucleus. State an appropriate unit for your answer.

density = mass / volume

m = (23 x 1.673 + 28 x 1.675) x 10-27

m = 8.5 x 10-26 kg

V = 4/3 π r3

V = 4/3 π (5.3 x 10 -15 )3

V = 6.24 x 10-43 m3


ρ = m/V

ρ = 8.5 x 10-26/6.24 x 10-43= 1.37 x 10 17

ρ = 1.4 x 10 17kg m-3

[3 marks]

(Total 8 marks)