Question

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

A) .57 grams
B) .70 grams
C) 2.25 grams
D) .75 grams

Answer 1

D. 0.75 grams

Step-by-step 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 ((1)/(2) \right )^{(t)/(t_(1/2)) }`

For two half lives, t = 2 ×
`t_((1/2))`

∴ t = 2 × 15 = 30

`(t)/(t_((1/2))) = (30)/(15) = 2`

`\therefore N(t) = 3 *\left ((1)/(2) \right )^2 = 0.75`

∴ The amount left, N(t) = 0.75 grams