(Please explain steps next to the work be shown and why we do those steps in ord
ID: 515182 • Letter: #
Question
(Please explain steps next to the work be shown and why we do those steps in order to come to a solution.)
Radioactive decay can be modeled by the function A(T)=C e^kt , where C is the starting mass (amount), k is the relative growth rate (which will be negative since we are talking about decay) , t is the time elapsed and A is the mass of radioactive component remaining.
A) The half life of the radioactive material cesium 137 is 30 years. Suppose we begin with a 100 mg sample. Find the relative growth rate of casium - 137.
B) At what rate is the mass decreasing, in mg/year, after 50 years? Round your answer to 4 decimal places.
Explanation / Answer
Given:- A(T)=C*e kt
t(half life time)=30 years, C=100gm
A) Relative growth rate of casium= K
at half life time t=t1/2 , the mass become half A(T)=C/2
C/2= C*ekt1/2
1/2= ekt1/2
taking log on both side
ln(1/2)=kt1/2
-0.6931=k*30
k= -0.02310 unit per year
The negative sign indicates the decay in mass with time.
B) k=?, at t=50 year C=100gm
The rate of decay is constant term independent of time and initial mass, so the rate at which mass is decreasing after 50 years is same as above rate constant (k)
rate of decay =k=0.02310 mg per year
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