Q10.

(a) Sketch, using the axes provided, a graph of neutron number, N, against proton number, Z, for stable nuclei over the range Z = 0 to Z = 80. Show suitable numerical values on the N axis.

N increases as Z increases - Graph should pass through N = 10 when Z = 10

N = (anywhere between 115 to 125) when Z = 80

The line should gently curve upwards - not be straight! They are expecting you to know that Z=80 will be about N=120 for stability - it is actually just short of that!

(2 marks)

(b) On the graph indicate, for each of the following, a possible position of a nuclide that may decay by

(i) emission, labelling the position with W,

W should be placed at a value of Z that is greater than 60 just (within one diagonal of a square) below the line

α particles are released from the nucleus when there are too many protons within the nucleus for stability and there is too much mass. The emitter will therefore be 'high up' on the graph and on the right or the line (Z value too big for stability).

(ii) emission, labelling the position with X,

X just (within one diagonal of a square) above line

Beta emission occurs when there are too few protons for stability. It will therefore be on the left of the line, so that after emission the point will move to a higher proton number value and get closer to the line.

(iii) emission, labelling the position with Y.

Y just (within one diagonal of a square) below line

Positron emission occurs when there are too many protons for stability, but the mass of the nucleus is not great. It will therefore be on the right of the line, so that after emission the point will move to a lower proton number value and get closer to the line.

(3 marks)

(c) The isotope decays sequentially by emitting particles and particles, eventually forming the isotope . Four particles are emitted in the sequence. Calculate the number of particles in the sequence.

Only alphas change the nucleon number:

4 alphas will reduce the nucleon number by 16 (222 - 16 = 206)

Those 4 alphas will reduce the proton number by 2 x 4 = 8

80 - 8 = 78

Alpha emission will change the nucleon and proton number - the examiners want to see your reasoning.

Betas will increase the proton number by 1.

The final proton number is 82 therefore there must be

82 - 78 = 4 beta particle emissions.

(2 marks)

(d) A particular nuclide is described as proton-rich. Discuss two ways in which the nuclide may decay.

Decay happens so that the radio-nucleus will move closer to line of stability - reducing the proton to neutron ratio is reduced.

You should discuss two of the following four processes:

• β+ (positron) emission occurs for proton rich isotopes that are light (Z < 60) - a proton changes to a neutron reducing the proton number.
• Alpha particle emission occurs for proton rich heavy nuclei (Z > 60). An alpha particle emission reduces the mass of the nucleus by 4 and the number of protons by 2.
• Proton emission only occurs if the nuclide is very proton rich. This makes the nucleus highly unstable. Proton emission is a very rare process as the electrostatic repulsion has to overcome the strong nuclear force.
• Electron capture involves the nucleus capturing an electron which then combines with a proton, resulting in a proton changing into a neutron.

Marking: listing two processes discussing each of the two processes

(3 marks)

(Total 10 marks)