Answer:
0.186 (18.6%)
Explanation:
The amount of mass of a radioactive isotope after a certain time t is given by the decay equation:
[tex]m(t)=m_0 e^{-\lambda t}[/tex]
where
[tex]m_0[/tex] is the mass of the isotope at time t = 0
[tex]m(t)[/tex] is the mass of the isotope at time t
[tex]\lambda[/tex] is the decay constant of the isotope
t is the time
The equation can be rewritten as
[tex]\frac{m(t)}{m_0}=e^{-\lambda t}[/tex]
Where the term on the left represents the fraction of isotope left after time t.
In this problem, we have:
[tex]\lambda=0.056 y^{-1}[/tex] is the decay constant of the isotope
We want to find the fraction of isotope left after time
t = 30 y
Substituting, we find:
[tex]\frac{m(t)}{m_0}=e^{-(0.056)(30)}=0.186 = 18.6\%[/tex]
