Answer to Question #88395 in Atomic and Nuclear Physics for Sydnee

Question #88395
The half-life of Yttrium-91 is 59 days. How much of a 90.3 g sample of Yttrium-91 will remain after 324 days?

(answer is in grams, no units required)
1
Expert's answer
2019-04-23T11:05:21-0400

Let’s use the formula for radioactive decay:


N=N0eλt,N = N_0e^{- \lambda t},

here, N0=90.3gN_0 = 90.3 g is the initial amount of Yttrium-91, NN is the amount of Yttrium-91 that will remain after 324 days, λ=0.693/T1/2\lambda = 0.693/T_{1/2} is the decay rate, T1/2=59daysT_{1/2} = 59 days is the half-life of Yttrium-91 and t=324dayst = 324 days is the time elapsed.

Then, we get:


N=N0eλt=90.3ge0.693324days59days=2.0g.N = N_0e^{- \lambda t} = 90.3 g \cdot e^{- \dfrac{0.693 \cdot 324 days}{59 days} } = 2.0 g.

Answer:

N=2.0g.N = 2.0 g.  


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