Question

The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 8.1% per day. find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay).

Answer 1

The general equation for radioactive decay is;
N = N₀e^(-λt)
x - decay constant (λ) - rate of decay 
t-  time 
N - amount remaining after t days , since we are calculating the half life, amount of time it takes for the substance to to be half its original value, its N₀/2
N₀ - amount initially present 
substituting the values 
N₀/2 = N₀e^(-0.081t)
0.5 = e^(-0.081t)
ln (0.5) = -0.081t
-0.693 = -0.081t
t = 0.693 / 0.081 
  = 8.55
half life of substance is 8.55 days