The half-life of francium-212 is 19 minutes. How many minutes will it take for 100 gram of this isotope to decay to 12.5 grams?

57 mins

Explanation:

From the question given above, the following data were obtained:

Half life (t₁/₂) = 19 mins

Original amount (N₀) = 100 g

Amount remaining (N) = 12.5 g

Time (t) =?

Next, we shall determine the number of half-lives (n) that wound have elapse for 12.5 g of the sample to remain. This can be obtained as follow:

Original amount (N₀) = 100 g

Amount remaining (N) = 12.5 g

Number of half-lives (n) =?

N = 1/2ⁿ × N₀

12.5 = 1/2ⁿ × 100

Cross multiply

12.5 × 2ⁿ = 100

Divide both side by 12.5

2ⁿ = 100 /12.5

2ⁿ = 8

Express 8 index with 2 as the base

2ⁿ = 2³

n = 3

Finally, we shall determine the time taken for 100 g of the isotope to decay to 12.5 g. This can be obtained as follow:

Half life (t₁/₂) = 19 mins

Number of half-lives (n) = 3

Time (t) =?

t = n × t₁/₂

t = 3 × 19

t = 57 mins

Thus, it will take 57 mins 100 g of the isotope to decay to 12.5 g.

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3 1/4 %

explanation: