Question

These exercises use the radioactive decay model. The mass m(t) remaining after t days from a 40-g sample of thorium-234 is given by m(t)=40e⁻⁰.⁰²⁷⁷ᵗ. Find the half-life of thorium-234.

Answer 1

The half-life of thorium-234 is approximately 25.03 days.

Step-by-step explanation:

To find the half-life of thorium-234 using the given equation m(t) = 40e⁻⁰.⁰²⁷⁷ᵗ, we need to determine the value of t when m(t) is equal to half of the initial mass of the sample, which is 40 g.

Setting m(t) = 20 and solving for t, we have:

20 = 40e⁻⁰.⁰²⁷⁷ᵗ

Take the natural logarithm of both sides:

ln(20/40) = -0.0277t

-0.693 = -0.0277t

Solving for t, we get:

t ≈ 25.03 days

Therefore, the half-life of thorium-234 is approximately 25.03 days.