State a nuclear equation to show the decay of lutetium-177.

The half-life of lutetium-177 is 6.73 days. Determine the percentage of a sample of lutetium-177 remaining after 14.0 days.

Explain the low environmental impact of most medical nuclear waste.

\({}_{71}^{177}{\text{Lu}} \to {}_{71}^{177}{\text{Hf}} + {}_{ - 1}^0{\text{e}}\) «+ \(\nu \)»

Hf

correct A and Z AND beta product

Accept “β/ β^–/e/e^–” for “\({}_{-1}^{~0}{\text{e}}\)”.

Accept “¹⁷⁷Lu → ¹⁷⁷Hf + e^– «+ \(\nu \)»”.

number of half-lives = \(\frac{t}{{{t_{^{\frac{1}{2}}}}}}\) = 2.08

OR

\(\frac{{N\left( t \right)}}{{{N_0}}} = {0.5^{\frac{{14.0}}{{6.73}}}}\)

OR

\(\lambda  = \) «\(\frac{{{\text{ln}}2}}{{{t_{^{\frac{1}{2}}}}}} = \frac{{{\text{ln}}2}}{{6.73}} = \)» 0.103 «day^–1»

OR

\(\frac{{N\left( t \right)}}{{{N_0}}} = {e^{ - 0.103\, \times 14.0}}\)

23.6 «%»

Award [2] for correct final answer.

Any two of:

emits weak ionising radiation

OR

low activity/radioactivity

can be stored until material becomes inactive AND then disposed with normal waste

«isotopes» have short lives

OR

exist for a short period of time

Award [1 max] for “low-level waste/LLW”.

[Max 2 Marks]