Question

Element X is a radioactive isotope such that every 26 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 680 grams, how much of the element would remain after 19 years, to the nearest whole number?

Answer 1

410 g

Explanation:

Radioactive decay can be modeled by an exponential equation. The amount remaining (y) after a time period (t) can be expressed in terms of the initial amount (a) and the half-life (h).

y = a(1/2)^(t/h)

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We can use this equation with the given values to find the amount remaining.

y = (680 g)(1/2)^((19 yrs)/(26 yrs)) ≈ (680 g)(0.602583)

y ≈ 410 g

About 410 grams of element X will remain after 19 years.