Question

The half life of Radium 226 is 1590 years. Because the rate of decay is proportional to the amount of material present, the radioactive decay will be modelled by an exponential "e" function.
(i) If the initial mass of Radium 226 present was 100g, write an exponential function R(t) that will describe the mass of Radium 226 remaining after t years with a decay rate of k.
(ii) Find the value of k (correct to 8dp)
(iii) How long will it take for the original mass of 100g to reduce to 30g?

Answer 1

so do you know what the simple exponential decay model looks like...?

Answer 2

R(t)=Ae^kt

Answer 3

So I've got R(t)=10e^kt

Answer 4

well I use a slightly different formula

\[A = A_{0} e^{kt}\]

where A is the population and \[A_{0} = ~initial ~population\]

t = time and k is the constant of decay

so then

\[A = 100e^{kt}\]

so that's the 1st part done.

to find k, use the information given to you

half life is 1590 years

so quantity is reduced to 50 gms after 1590 years

so

\[50 = 100e^{1590 \times k}\]

now solve for k

hope it helps

Answer 5

Just wondering, how did you get 50gms after 1590 years?

Answer 6

the term half life... means that the quantity gets to half it's original size...

so half of 100gm is 50gm.

and the time to reach half life is 1590 years

Answer 7

Thanks!