Formula for Radioactive Decay

Question

The half-life of Radium-226 is 1590 years. How long will it take for 60 percent of a 200 gram sample to decay?

Answer 1

You can use the formula A = P₀ (1/2)^t/k

 

where A = the amount remaining, P₀ = the initial amount of the substance, t = the amount of time, and k = the half-life of the substance

 

We know that P₀ = 200 gm, A = 40% of 200 gm (that's how much of the substance will remain after 60% has decayed) = 0.40 * 200 = 80 gm, k = 1590 years, and t is the quantity that we are attempting to find.

 

80 = 200(1/2)^t/1590

 

2/5 = (1/2)^t/1590

 

Take the ln of both sides

 

ln (2/5) = ln (1/2)^t/1590

 

ln(2/5) = t/1590 * (ln (1/2))

 

[ln (2/5)]/[ln (1/2)] = t/1590

 

You can use your calculator to help you solve this now for t.