Question

If the half life of iridium-182 is 15 years, how much of a 3 gram sample is left after 2 half-lives?

Answer 1

Answer:

D. 0.75 grams

Explanation:

The data given on the iridium 182 are;

The half life of the iridium 182, $t_{(1/2)}$ = 15 years

The mass of the sample of iridium, N₀ = 3 grams

The amount left, N(t) after two half lives is given as follows;

$N(t) = N_0 \left (\dfrac{1}{2} \right )^{\dfrac{t}{t_{1/2}} }$

For two half lives, t = 2 × $t_{(1/2)}$

∴ t = 2 × 15 = 30

$\dfrac{t}{t_{(1/2)}} = \dfrac{30}{15} = 2$

$\therefore N(t) = 3 \times\left (\dfrac{1}{2} \right )^2 = 0.75$

∴ The amount left, N(t) = 0.75 grams