Yttrium-90 is used in treating certain cancers.

Formulate a nuclear equation for the beta decay of yttrium-90.

Lutetium-177 is a common isotope used for internal radiation therapy.

Suggest why lutetium-177 is an ideal isotope for the treatment of certain cancers based on the type of radiation emitted.

Calculate the rate constant, \(\lambda \), in day⁻¹, for the decay of iodine-131 using section 1 of the data booklet.

Calculate the time, in days, for 90% of the sample to decay.

A breathalyser measures the blood alcohol content from a breath sample. Formulate half-equations for the reactions at the anode (negative electrode) and the cathode (positive electrode) in a fuel cell breathalyser.

⁹⁰Y → ⁹⁰Zr + β^–

Accept β, e or e^–.
Accept ⁹⁰Y → ⁹⁰Zr + β^– + v

[1 mark]

beta-radiation/emission AND targets tumour/cancer cells
OR
beta-radiation/emission AND limited damage to healthy cells/tissues
OR
beta-radiation/emission AND produces «small amount of» gamma-rays «for visualizing tumours/monitoring treatment»

[1 mark]

\(\lambda \left( { = \frac{{\ln 2}}{{{t_{\frac{1}{2}}}}} = \frac{{0.693}}{{8.02{\text{ }}day}}} \right) = 8.64 \times {10^{ - 2}}/0.0864\) «day⁻¹»

[1 mark]

ALTERNATIVE 1:
«N₀ = initial amount = 100%»

N «= 100 – 90» = 10% at time t

«\(\ln \left( {\frac{{100}}{{10}}} \right) = 2.303 = 0.0864t\)»

«\(t = \frac{{2.303}}{{0.0864{\text{ da}}{{\text{y}}^{ - 1}}}} = \)» 26.7 «days»

Accept 26.6 or 27 «days»
Award [2] for correct final answer.

ALTERNATIVE 2:
«N_t = N₀(0.5)ⁿ where n = number of half-lives»

10 = 100(0.5)ⁿ

«\(\log \left( {\frac{1}{{10}}} \right) = n \times \log \,0.5\)»

«\( - 1 = n\left( { - 0.301} \right)/n = \frac{1}{{0.301}}\)»

«t \( = \frac{1}{{0.301}} \times 8.02 = \)» 26.6 «days»

Accept 26.7 or 27 «days»

Award [2] for correct final answer.

[2 marks]

Anode (negative electrode): C₂H₅OH + H₂O → CH₃COOH + 4H⁺ + 4e^–

Cathode (positive electrode): O₂ + 4H⁺ + 4e^– → 2H₂O

[2 marks]