Question

Lanthanum-138 has a half-life of 105 billion years. after 525 billion years, how much of a 240 g sample of this radioisotope will remain? grams

Answer 1

The amount of the 240 g sample of the radioisotope that will remain after 525 billion years is 7.5 g

How to the number of half-lives that has elapsed

• Half-life (t½) = 105 billion years
• Time (t) = 525 billion years
• Number of half-lives (n) = ?

n = t / t½

n = 525 / 105

n = 5

How to determine the amount remaining

• Original amount (N₀) = 240 g
• Number of half-lives (n) = 5
• Amount remaining (N) = ?

N = N₀ / 2ⁿ

N = 240 / 2⁵

N = 240 / 32

N = 7.5 g

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