Answered

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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

Sagot :

Answer:

D. 0.75 grams

Explanation:

The data given on the iridium 182 are;

The half life of the iridium 182, [tex]t_{(1/2)}[/tex] = 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;

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

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

∴ t = 2 × 15 = 30

[tex]\dfrac{t}{t_{(1/2)}} = \dfrac{30}{15} = 2[/tex]

[tex]\therefore N(t) = 3 \times\left (\dfrac{1}{2} \right )^2 = 0.75[/tex]

∴ The amount left, N(t) = 0.75 grams

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