After two half-lives, how much of the original material has decayed? 25 percent 50 percent 75 percent 100 percent

We can start this problem by solving the first half-life assuming the arbitrary condition stating that the initial concentration has a value of 100M, thus, for the first half-life, the concentration dwindles to 50M. Afterwards, the second half-life yields a concentration of 25M, meaning that the 75% of the material has decayed up to the second half-life, of course, the half of the result from the first half-life.

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Eduard22sly Eduard22sly · Answer 2 · 2021-10-01T17:26:31+02:00

The correct answer to the question is 75 percent.

Let the original amount be 100%

From the question given above, the following data were:

Number of half-lives (n) = 2

Amount that has decayed =?

Next, we shall determine the amount remaining after 2 half-lives.

Original amount (N₀) = 100%

Amount remaining (N) =?

The amount remaining can be obtained as follow:

[tex]N = \frac{N_{0} }{2^{n}} \\\\N = \frac{100}{2^{2}} \\\\N = \frac{100}{4}\\\\[/tex]

N = 25%

Finally, we shall determine the amount that has decayed.

Original amount (N₀) = 100%

Amount remaining (N) = 25%

Amount that has decayed =?

Amount that have decayed = (Original amount) – (Amount remaining)

Amount that have decayed = 100 – 25

Amount that have decayed = 75%

Thus, 75% of the original material has decayed.

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