Use the exponential decay model, A=A o e^kt. The half-life of thorium-229 is 7310 years. How long will it take for a sample of this substance to decay to 20% of its original amount?

Question

Use the exponential decay model, A=A o e^kt. The half-life of thorium-229 is 7310 years. Round answers to 6 decimal place.

Answer 1

t = 7310(ln.2/ln.5) = about 16,973.2944

Answer 2

Here's the long way: solve for k first, given the half life of 7310 yrs.

Assume A₀ = 1gm

A/A₀ = 1/2 = 1e^7310k Take the ln of both sides: ln(0.5) = 7310k

k = ln(0.5)/7310 = -0.693147/7310 = -0.000094822

Then use ratio of 20% to find t: 0.2 = 1e^{-0.000094822t}

ln(0.2) = -0.000094822t → -1.6094379 = -0.000094822t → t ≅ 16,973 yrs. (Don't see why answer must be rounded to 6 decimal places!)

Or use Mark M's approach: 0.2 = (0.50)^t/7310

Answer 3

Since the half -life is provided why not use that formula?

0.20 = (0.50)^t/7310