The half-life of radium-226 is 1600 years

Question

(a) What is the exponential decay rate? Round to 5 decimal Places

(b) Suppose we have 20 mg sample. How much of the sample will remain after 3000 years? Round to two decimal places

Answer 1

A = A₀e^rt

 

0.5A = A₀e^r(1600)    divide both sides by A₀

0.5 = e^1600r            take natural log of both sides

ln 0.5 = 1600r         calculate ln

-0.693 ≈ 1600r        divide both sides by 1600

-0.000433 ≈ r

 

The exponential decay rate is approximately -0.04%.

 

For letter (b)

 

A = 20e^{(-0.004)(3000)}