Question

If 2g of the original 64g remains and the half-life is 1,864 years, how much total time has passed?

Answer 1

The total time that has passed is 9320 years.

To obtain the answer to the question given above, we'll begin by calculating the number of half-lives that has elapsed. This can be obtained as follow:

Amount remaining (N) = 2 g

Original amount (N₀) = 64 g

Number of half-lives (n) =?

N₀ × 2ⁿ = N  

2 × 2ⁿ = 64

2ⁿ = 64/2

2ⁿ = 32

Express 32 in index form with 2 as the base

2ⁿ = 2⁵

n = 5

Thus, 5 half-lives gas elapsed.

Finally, we shall determine the total time that has passed. This can be obtained as follow:

Number of half-lives (n) = 5

Half-life (t½) = 1864 years

Time (t) =?

t = n × t½

t = 5 × 1864

t = 9320 years

Therefore, the total time that has passed is 9320 years

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