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HELP ME PLEASEEE!!!!

How long will it take for 10% of a 1000-gram sample of uranium-235 to

In(0.5)

decay? Use the decay formula A(t) = Age- t.

T

The half-life for uranium-235 is 703,800,000 years.

User SalGad
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2 Answers

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20 votes

Final answer:

It will take approximately 106.6 million years for 10% of a 1000-gram sample of uranium-235 to decay, calculated using the radioactive decay formula and the half-life of uranium-235.

Step-by-step explanation:

The question asks how long it will take for 10% of a 1000-gram sample of uranium-235 to decay, given that the half-life of uranium-235 is 703,800,000 years. Using the decay formula A(t) = A0e-(ln(2)t/T), where A(t) is the amount of substance remaining after time t, A0 is the initial amount, T is the half-life, and ln is the natural logarithm:

  1. First, determine the remaining amount of uranium-235 after decay: A(t) = 1000 g * (1 - 0.10) = 900 g.
  2. Use the decay formula to solve for time t:
    900 = 1000 * e-(ln(2)t/703800000)
    ln(900/1000) = -(ln(2)t/703800000)
    t = (ln(1000/900) * 703800000) / ln(2)
  3. Calculate t: t ≈ (0.10536 * 703800000) / 0.69315 ≈ 106,594,859.6 years.

It will take approximately 106.6 million years for 10% of a 1000-gram sample of uranium-235 to decay.

User PranavPinarayi
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19 votes
19 votes

Answer: A: 106,979,777 years

Step-by-step explanation:

User Dom Free
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