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radon-222 has a half life of 3.82 days. how much of a 100-g sample of radon-222 will remain unchanged after 7.64 days
A.100 g
B.50 g
C. 75 g
D. 25 g

Respuesta :

thankins2017p7070c
The half-life of a substance describes the time in which it takes for half of the radioactive isotope to decay into another form. In your question, it says that the half life of radon-222 is 3.82 days; in a 100g sample of radon, 3.82 days pass and 50g of that isotope is left.

7.64 days is the equivalent to two half lives (7.64/3.82), so only half of half of 100%, or 25%, of the isotope would remain. The answer is D.
Eduard22sly

The mass of radon-222 that will remain unchanged after 7.64 days is 25 g

The correct answer to the question is Option D. 25 g

  • We'll begin by calculating the number of half-lives that has elapsed. This can be obtained as follow:

Half-life (t½) = 3.82 days

Time (t) = 7.64 days

Number of half-lives (n) =?

[tex]n = \frac{t}{t_{1/2}}\\\\n = \frac{7.64}{3.82} \\\\[/tex]

n = 2

Thus, 2 half-lives has elapsed.

  • Finally, we shall determine the amount that will remain unchanged after 7.64 days. This can be obtained as follow:

Original amount (N₀) = 100 g

Number of half-lives (n) = 2

Amount remaining (N) =?

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

N = 25 g

Thus, 25 g of the radon-222 will remain unchanged after 7.64 days.

The correct answer to the question is Option D. 25 g

Learn more: https://brainly.com/question/14883322

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