The age in years of a rock specimen that contains 60% of the original number of uranium atoms is 3.3 x 10⁹yr.
Half life is the time taken by a radioactive material for the radioactivity of to reduce by half its original value.
The half life equation is:
N/N₀ = e^(-λt)
where N is the final amount, N₀ is the initial amount, λ is the decay constant, and t is the age of specimen.
decay constant λ = 0.693/ T1/2
Given is the half life for the alpha decay of uranium is 4.47×10⁹yr .
decay constant λ = 0.693/ 4.47×10⁹ =0.155 x 10⁻⁹ /s
To find the age of rock specimen,
Substitute the value of N /N₀ =0.6 (for 60%), and T = 2020 days.
-λt = ln ( N /N₀)
ln(0.6) = -(0.55 x 10⁻⁹xt)
t = 3.3 x 10⁹yr
Thus, the age of rock specimen is 3.3 x 10⁹yr
Learn more about half life.
https://brainly.com/question/24710827
#SPJ1
