Half Life Problem Help?

Question

Please tell and show how you got your answer, I dont just want the answer, i want an explanation.

Q1: How many half lives have passed if a radioactive sample has decayed from 480g to 15g ?

Q2: After 36 years, a radioactive sample has decayed from 400g to 25g. What is the length of its half life.

Q3: A radioactive sample has decayed over 25 years. The amount of the sample that is radioactive has gone from 240g to 15g. What is the length of its half life?

Please try to help with as many of the following Q's you can!

Anonymous · Accepted Answer

Q1: After each half life the sample decays by half (/2)
480g/2^n = 15g
480=15*2^n
ln480=ln15+nln2
n=(ln480-ln15)/ln2
n=5 
∴5 half-lives have past.

Q2: Using the same principles as Q1 we find the number of half lives.
400/2^n=25g
...
n=(ln400-ln25)/ln2
n=4
∴ the length of the half life is 36 years/4 = 9 years

Q3: Same as Q2
n=(ln240-ln15)/ln2=4
length of half life = 25/4 = 6.25 years

Half Life Problem Help?

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