Question

If an original sample of U238 has a mass of 24 grams, what is the total amount of U238 left after 18 billion years? Show your work!

Answer 1

The total amount of U-238 left after 18 billion years is 1.5 gm

- The half life of U-238 is 4.5 billion years, i.e., T1/2 = 4.5 × 10⁹ years

- By using formula, we have

T1/2 = 0.693/k

4.5 × 10⁹ = 0.693/k

k = 0.693/4.5 × 10⁹

k = 0.154  × 10⁻⁹ yr⁻¹

- Here, time taken, t = 18 billion years = 18 × 10⁹ years

[R]₀ = 24 gram

Using equation, we have

k = (2.303/t)log([R]₀/[R])

0.154  × 10⁻⁹ = (2.303/ 18 × 10⁹) log (24/[R])

log 24 - log [R] = 1.204

log [R] = 1.38 - 1.204 = 0.176

[R] = antilog 0.176 = 1.499 gm ≈ 1.5 gm