Solutions: Radioactivity Questions
(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
(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
(ii) emission, labelling the position with X,
X just (within one diagonal of a square) above line
(iii) emission, labelling the position with Y.
Y just (within one diagonal of a square) below line
(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
Betas will increase the proton number by 1.
The final proton number is 82 therefore there must be
82 - 78 = 4 beta particle emissions.
(d) A particular nuclide is described as proton-rich. Discuss two ways in which the nuclide may decay.
- 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
(Total 10 marks)