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QHi there, I have an exam today and I was doing a practise exam where I came across this question and was unable to solve it

Hi there, I have an exam today and I was doing a practise exam where I came across this question and was unable to solve it. Could one of the tutors please help me with it, I'd be more than grateful!!!!


Scientists have 50g of a radioactive element that decomposes with a half-life of 15 seconds. (3 marks:1 mark each)

a) Write an equation that predicts the amount of the element remaining as a function of time.

b) How much of the element would remain after 2 minutes?

c) How long would the element take to decompose to the point where there is only 0.01g remaining?

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#1JaredAnswered at 2012-12-04 05:41:00
Scientists have 50g of a radioactive element that decomposes with a half-life of 15 seconds. (3 marks:1 mark each) a) Write an equation that predicts the amount of the element remaining as a function of time. P = Ce^(kt) 25 = 50e^(k*15) 25/50 = e^(k*15) 1/2 = e^(k*15) ln(1/2) = 15k ln(1/2)/15 = k Your equation then: P = 50e^[(ln(1/2)/15)t] . b) How much of the element would remain after 2 minutes? 2 minutes = 2*60 = 120 secs plug it into the equation: P = 50e^[(ln(1/2)/15)t] P = 50e^[(ln(1/2)/15)120] P = 50(.00390625) P = .195 grams . c) How long would the element take to decompose to the point where there is only 0.01g remaining? 0.01 = 50e^[(ln(1/2)/15)t] 0.0002 = e^[(ln(1/2)/15)t] -8.5172 = (ln(1/2)/15)t -8.5172/(ln(1/2)/15) = t 184.32 secs = t
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