The isotope tritium (hydrogen-3) has a radioactive half-life of 12 days. 

(i) State what is meant by the term isotope.

(ii) Define radioactive half-life.

Tritium may be produced by bombarding a nucleus of the isotope lithium-7 with a high-energy neutron. The reaction equation for this interaction is

\[{}_3^7{\rm{Li}} + {}_0^1{\rm{n}} \to {}_1^3{\rm{H}} + {}_Z^4{\rm{X}} + {}_0^1{\rm{n}}\]

(i) Identify the proton number Z of X.

(ii) Use the following data to show that the minimum energy that a neutron must have to initiate the reaction in (b)(i) is about 2.5 MeV.

Rest mass of lithium-7 nucleus       = 7.0160 u
Rest mass of tritium nucleus           = 3.0161 u
Rest mass of X nucleus                  = 4.0026 u

Assuming that the lithium-7 nucleus in (b) is at rest, suggest why, in terms of conservation of momentum, the neutron initiating the reaction must have an energy greater than 2.5 MeV.

Define linear momentum.

A nucleus of tritium decays to a nucleus of helium-3. Identify the particles X and Y in the nuclear reaction equation for this decay.

\[{}_1^3{\rm{H}} \to {}_2^3{\rm{He}} + {\rm{X}} + {\rm{Y}}\]

X:

Y:

A sample of tritium has an activity of 8.0×10⁴ Bq at time t=0. The half-life of tritium is 12 days.

(i) Using the axes below, construct a graph to show how the activity of the sample varies with time from t=0 to t=48 days.

(ii) Use the graph to determine the activity of the sample after 30 days.

(iii) The activity of a radioactive sample is proportional to the number of atoms in the sample. The sample of tritium initially consists of 1.2×10¹¹ tritium atoms. Determine, using your answer to (e)(ii) the number of tritium atoms remaining after 30 days.

(i) nuclides/atom/element/nucleus/nuclei that have different nucleon/neutron numbers but same proton number/are same element / OWTTE;

(ii) the time taken for the activity (of a radioactive sample) to decrease by half / the time taken for half the (initial) number of radioactive nuclei/atoms/mass to decay; (“radioactive” must be seen in alternative answer)

(i) 2;

(ii) (mass difference=)7.0160 – [3.0161+ 4.0026]= (–)2.7x 10^-3u;
(energy required= )(–)2.7x10^-3x931.5 or 2.5151(MeV) ;
(≈ 2.5 MeV)

Allow unit conversions via mass and mc² .
Must see either answer to 3+sf or subtraction or use of mc² to award 2^nd mark.

2.5MeV must be converted to mass (in the interaction) / otherwise the products would not be moving;
(to conserve momentum) final products must have total momentum equal to that of incoming neutron (so extra energy is required) / OWTTE;

product of mass and velocity; (do not allow “speed”)

Accept symbols if defined correctly.

\({}_1^3{\rm{H}} \to {}_2^3{\rm{He}} + {\beta ^{\rm{ - }}} + \bar v\)
β^- or \({}_{ - 1}^0{\rm{e}}\) or e^- or electron or beta particle;
\(\bar v\) or \({}_0^0\bar v\) or antineutrino;
Allow answers in either order.

(i)

five correct data points;
smooth curve through data points;
Do not allow ECF if incorrect points are plotted leading to a non-smooth curve.
Award full credit for correct curve even if the data points are not visible.

(ii) 1.4×10⁴ (Bq);
Allow correct reading from mis-drawn graph \( \pm \) 0.1.

(iii) number of atoms left=\(\frac{{1.2 \times {{10}^{11}} \times 1.4}}{8}\) or uses proportion or uses ln\(\left( {\frac{N}{{{N_0}}}} \right) =  - \lambda t\); (with correct values)
2.1×10¹⁰;
Award [2] for a bald correct answer.

(i) Although many were able to give a correct statement of the meaning of the term isotope there were a disappointing number who could not. In general, candidates should attempt to give clearer, more succinct definitions.

(ii) Equally, definitions of radioactive half-life were often weak, incomplete and confused, referring to the amount or mass of the total (rarely initial) substance rather than its activity. These are straightforward definitions to memorize and candidates would be well advised to spend time on this routine task.

(i) The proton number was almost invariably correct.

(ii) All the basics of this question were understood, the calculation was not well completed by many. Candidates need to understand that to gain full credit in response to “show that” they must convince the examiner that all steps are shown. This is best done by taking the calculation through to at least one more significant figure than is quoted in the question and explaining each line of calculation in words. Even strong candidates are not as careful as they could be about this.

This was another question where the candidates needed to articulate a logical argument. It was extremely poorly done. It would seem that candidates are muddled between the concepts of energy and momentum. There were attempts to gain a mark but candidates did not consider in the first instance why the neutron energy has to be greater than 2.5 MeV. This should not have been beyond the more able SL candidate.

Most could define linear momentum correctly using the terms mass and velocity.

 Failure to recognize that the antineutrino not the neutrino is produced marred this normally well-answered question.