- #1

moenste

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## Homework Statement

Potassium 44 (

^{44}

_{19}K) has a half-life of 20 minutes and decays to form

^{14}

_{20}Ca, a stable isotope of calcium.

(a) How many atoms would there be in a 10 mg sample of potassium 44?

(b) What would be the activity of the same?

(c) What would the activity be after one hour?

(d) What would the ratio of potassium atoms to calcium atoms be after one hour?

(N

_{A}= 6 * 10

^{23}mol

^{-1}.)

Answers: (a) 1.4 * 10

^{20}, (b) 7.9 * 10

^{16}Bq, (c) 9.8 * 10

^{15}Bq, (d) 1:7

I got every part except (d).

**2. The attempt at a solution**

(a) 44 g of Potassium 44 contain 6 * 10

^{23}atoms. (10 * 10

^{-3}) g of Potassium 44 contain ((10 * 10

^{-3}) / 44) * (6 * 10

^{23}) = 1.36 * 10

^{20}atoms.

(b) dN / dt = -λN = - ((ln 2) / (20 * 60)) * (1.36 * 10

^{20}) = -7.9 * 10

^{16}s

^{-1}-> 7.9 * 10

^{16}Bq

(c) A = A

_{0}e

^{-λt}= (7.9 * 10

^{16}) * e

^{-((ln 2) / (20 * 60)) * (60 * 60)}= 9.8 * 10

^{15}Bq

(d) For this part I am lost. Any ideas please? I did the same calculations for Calcium as in part (a-c) and compared the numbers and they all got me around 0.3 and not the 1:7 (0.14).