Question

Problem PageQuestion The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 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

8.55 days for a decay rate parameter of 8.1% per day

Explanation:

Assuming a decay rate parameter of 8.1% per day

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