Write the nuclear equation for this fission reaction.

Outline why the reaction releases energy.

The masses of the particles involved in this fission reaction are shown below.

Mass of neutron = 1.00867 amu
Mass of U-235 nucleus = 234.99346 amu
Mass of Ba-144 nucleus = 143.89223 amu
Mass of Kr-89 nucleus = 88.89788 amu

Determine the energy released, in J, when one uranium-235 nucleus undergoes fission. Use this data and information from sections 1 and 2 of the data booklet.

The critical mass for weapons-grade uranium can be as small as 15 kg. Outline what is meant by critical mass by referring to the equation in (a)(i).

The daughter product, ⁸⁹Kr, has a half-life of 3.15 min.

Calculate the time required, in minutes, for its radioactivity to fall to 10% of its initial value, using section 1 of the data booklet.

²³⁵U + ¹n → ¹⁴⁴Ba + ⁸⁹Kr + 3¹n   [✔]

greater binding energy per nucleon in products than reactants    [✔]

Note: Accept “mass of products less than mass of reactants” OR “mass converted to energy/E = mc²”.

«Δm  mass of reactants-mass of products»

Δm = «234.99346 – 143.89223 – 88.89788 – (2 × 1.00867) =» 0.18601 «amu»   [✔]

Δm = «0.18601 amu × 1.66 × 10⁻²⁷ kg amu^–1 =» 3.09 × 10^–28 «kg»    [✔]

E = «mc² = 3.09 × 10^–28 kg × (3.00 × 10⁸ m s^–1)² =» 2.78 × 10^–11 «J»    [✔]

Note: Award [3] for correct final answer.

mass/amount/quantity required so that «on average» each fission/reaction results in a further fission/reaction   [✔]

at least one of the «3» neutrons produced must cause another reaction    [✔]

Note: Accept “minimum mass of nuclear fuel needed for the reaction to be selfsustaining”.

$\lambda \left(=\frac{\ln 2}{t_{\frac{1}{2}}}=\frac{\ln 2}{3.15}\right)=0.220$ «min^–1»    [✔]

$t\left(=-\frac{1}{\lambda }\ln \frac{N}{N_0}=-\frac{\ln 0.1}{0.220}\right)=10.5$ «min»    [✔]

Note: Award [2] for correct final answer.

Required candidates to write a nuclear equation for a fission reaction with the question indicating that ²³⁵U was bombarded with a neutron to produce ¹⁴⁴Ba and ⁸⁹Kr. Despite this, some candidates did not include the initial neutron or omitted neutrons completely.

Outlining why the fission reaction releases energy was challenging. Some candidates simply said the reaction was exothermic. Some said that the products were smaller than the reactant. Very few candidates referred to binding energy per nucleon.

The calculation of the energy released in was done reasonably well. Some candidates answered this very well and scored full marks. However, many scored 1 or 2 marks out of 3 through ECF marks. Common errors were incorrect calculation of mass in amu, or omission of converting amu to kg. Here, it was apparent that good setting out of calculations was effective in scoring for partially correct responses.

The meaning of critical mass was answered reasonably well with most candidates scoring at least 1 out of 2.

The calculation of time taken for radioactivity to fall to 10% of its initial value was answered very well.