Question #114707
Sodium-24 has a half-life of 15 hours. If a sample of sodium-24 has an original activity of 500 Bq, what will its activity be after 60 hours?
1
Expert's answer
2020-05-08T16:18:49-0400

We know that after 15 hours the half of initial number of atoms will decay. Therefore, we can write (see https://en.wikipedia.org/wiki/Half-life#Formulas_for_half-life_in_exponential_decay)

N(T)=N(0)(12)TT1/2,N(T) = N(0)\cdot \left( \dfrac12\right)^{\frac{T}{T_{1/2}}}, where T1/2T_{1/2} is the half-life.


Activity is proportional to the number of atoms not decayed yet. So, we should determine fraction N(T)N(0)=N(60)N(0)=(12)6015=(12)4=116.\dfrac{N(T)}{N(0)} = \dfrac{N(60)}{N(0)} = \left( \dfrac12\right)^{\frac{60}{15}} = \left( \dfrac12\right)^4 = \dfrac{1}{16}.

Therefore, the activity after 60 hours will be 116\dfrac{1}{16} of the original activity or 500116=31.25500\cdot\dfrac{1}{16} = 31.25 Bq.


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