Question

after 1 year, 80% of the initial amount of a radioactive substance remains. what is the half-life of the substance? half-life is

Answer 1

If a radioactive substance remains 80% of the initial amount then the half life of the radioactive substance is 2.5 years.

Given 80% of the initial amount of a radioactive substance remains.

If after 1 year the value or weight of the radioactive substance remains 80% means the rate of disappearing is 20% per annum.

If we clearly observe then it is forming a geometric progression and the rate is 80%.

Geometric progression will be if we assume the initial quantity be 100

is:

100,80,64,.........

we have to calculate the value of years in the value of term is 0.

the value of nth term of a geometric progression is $ar^{n-1}$

so,

r is 0.8

100*$0.8^{n-1}$=0

$0.8^{n-1}$=0

if we calculate this we will find n-1=11

n=12

So the full life of radioactive substance is 12 and the half life will be 6 years.

Learn more about geometric progression here https://brainly.com/question/12006112

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