DP Chemistry (last assessment 2024)

Question 17N.3.hl.TZ0.b

[Maximum mark: 2]

17N.3.hl.TZ0.b

Lutetium-177 is used in radiotherapy. It emits beta radiation when it decays.

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

[2]

Markscheme

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

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

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

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

23.6 «%»

Award [2] for correct final answer.

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