Identifying a Radioactive Material Using Half-Life Measurements

[Ramandeep]

the assignment is written as follows:
A parcel is attracting nervous attention at australian post. the parcel is radioactive and inspectors are trying to identify the material. Suppose they make the following measurements. There are 50 grams of the material and it's decaying at a rate of 0.25 grams per day.

One of the characteristics of radioactive materials is it's half life. That is the time it takes for half the material to decay. Below is a table giving the half-lives of common radioactive elements.

ISOTOPE HALF LIFE
Carbon-14 5730 years
Chlorine-36 301,000 years
Polonium-210 138 days
Phosphorus-32 14.2 days
Iodine-131 8 days
Uranium-238 4.5 x10years

Your task is to identify the material in the box assuming that the isotope will decrease to 25 grams. Using the ideas developed in class, it should be clear that an exponential equation would provide a good model for radioactive decay.

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so recently in class we've been learning about derivatives, logs, ln, etcc
please help me with full detail...i have no idea how to do this
THANKSSS

 

[HallsofIvy]

In order for what you wrote, we need to assume that the material is "decaying at a rate of 0.25 grams per day" right now, now in general. Radioactive materials decay at a rate proportional to the amount, not at a constant rate. Since there is, right now, 50 g of the substance and it is, right now, decaying at a rate of .25 g per day, it is decaying at a rate of .25/50= 0.005 times the amount.

That is, if Y is the amount at any time, we have dY/dt= -.005Y. You should be able to integrate that to get Y as an exponential. Then determine the time, in days, until there is exactly half left. That will give you the half life.

 

[Ramandeep]

Thankyou so much because that was really helpful. Ecspecially the first paragraph because it certified the calculations I had! Though I could not understand how to get half life of the suinstance still... So could you please just explain in more detail... This is all new to me, maths is not my forte haha.
Thanks :)

 

[Ramandeep]

Substance / material ****