We have to wait 5.57 half lives for a radioactive sample to drop to 2.10 % of its original activity.
To find the tike taken for the activity, we need to know about radioactivity and half-life.
What is radioactivity?
- Radioactivity is the rate of decay of a radioactive substance with respect to time.
- Mathematically, radioactivity is given as
R=R₀e^(-λ×t)
- From the above expression time is given as
t= 1/λ ln(R₀/R)
What is half-life?
- Half-life is the time taken for decay of radioactive sample to half of its initial value.
- Mathematically, half-life= ln2 / λ
What is the expression of time of activity in term of half-life?
- From the half-life expression, 1/λ=half-life/ln2.
- Putting the value of 1/λ in the expression of time of activity, we have
t=(half-life/ln2)×ln(R₀/R)
What is the time for radioactive sample to drop to 2.10 % of its original activity?
Here R=0.021R₀, so t= (half-life/ln2)×ln(R₀/0.021R₀)=5.57 half-lives
Thus, we can conclude that we have to wait 5.57 half lives for a radioactive sample to drop to 2.10 % of its original activity.
Learn more about radioactivity here:
https://brainly.com/question/11117468
#SPJ2
