After three half-lives, one-ninth of an original radioactive parent isotope remains, and eight-ninths has decayed into the daughter isotope. A. TrueB. False

Question

Kolby York

Physics

29 November, 07:58

After three half-lives, one-ninth of an original radioactive parent isotope remains, and eight-ninths has decayed into the daughter isotope. A. TrueB. False

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Answers (1)

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Moises Pierce · Answer 1

B. False

The true statement will be:

After three half-lives, one-eighth of an original radioactive parent isotope remains, and seven-eighth has decayed into daughter isotopes.

Explanation:

Half life means the time after which the amount of the given substance becomes half of its initial amount, by radiation.

Thus after each successive half life the material is halved or half of it is decayed, which leads to a general formula:

Remaining Amount = 1/2^n of parent isotope

where, n is the number of half lives passed. So, for three half-lives:

Remaining Amount = 1/2^3 of parent isotope

Remaining Amount = 1/8 of parent isotope

Thus, the decayed amount will be:

Decayed Amount = (1-1/8) of parent isotope

Decayed Amount = 7/8 of parent isotope

Thus, the given statement is B. False