The activity of a radioactive isotope decreases from 8000 to 10000 in 60 days_ The half life of isotope will be
Answers
Answer:
The activity of a radioactive isotope decreases from 8000 to 10000 in 60 days_ The half life of isotope will be
Given: The activity of a radioactive isotope decreases to 8000 from 10000 in 60 days.
To find: Half life of an isotope
Explanation: Half life of a radioactive isotope is given by : 0.69/k where k is the rate constant of the reaction.
Radioactivity of isotope is a first order reaction. The formula for first order reaction is as follows:
Remaining= Original * e^-kt
where t is the time taken in reaction which in this case is 60 days.
=> 8000= 10000 e^-60k
=>4/5 = e ^-60 k
=> ln (4/5) = -60k
=> -0.22 = -60k
=> k = 0.22/60 days
Now, half life = 0.69/k
= 0.69/(0.22/60)
= 69* 60 /22
= 188 days
Therefore, the half life of this isotope is 188 days.