Question

One of the nuclides in spent nuclear fuel is U-235 , an alpha emitter with a half-life of 703 million years.
How long will take for the amount of U-235 to reach 49.0% of its initial amount?

Answer 1

We use our equation for half-life to find k

ln(1/2) = -kt

We have that t = 703 million years

Therefore, we divide by 703 million, and we get:

k = 9.86 x 10^-10

Therefore, we now solve for A = .49, or 49%

ln(A/A_o) = -kt

ln(.49/1) = -(9.86 x 10^-10) (t)

-.71335 / -(9.86 x 10^-10) = t

7.235 x 10⁸ years, or

723,500,000, which makes sense as it should be just slightly over he half life of 703,000,000 years!