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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answer

fusion: the energy source of stars. the energy released from the collapse of the gas into a protostar causes the center of the protostar to become extremely hot. when the core is hot enough, nuclear fusion commences. fusion is the process where two hydrogen atoms combine to form a helium atom, releasing energy.

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