Radioactive Isotope Calculation: How Much Remains After 16 Days?

Question:

A scientist has a 10-mg sample of a radioactive isotope with a half-life of 8 days. After 16 days, how much of the radioactive isotope remains?

Answer:

The amount of the radioactive isotope remaining after 16 days is 2.5 mg.

Radioactive isotopes decay over time, and their remaining amount can be calculated using a specific formula. In this case, we have an initial amount of 10 mg and a half-life of 8 days for the radioactive isotope.

The formula used to calculate the remaining amount of a radioactive isotope after a certain time period is:

A = a * (1/2)^(t/h)

Where:

  • A is the amount remaining
  • a is the initial amount
  • t is the time elapsed
  • h is the half-life of the substance

Plugging in the values we have: A = 10 * (1/2)^(16/8) A = 10 * (1/2)^2 A = 10 * (1/4) A = 2.5 mg

Therefore, after 16 days, only 2.5 mg of the radioactive isotope remains. This calculation showcases the decay of radioactive isotopes over time and how the remaining amount can be determined based on the initial amount and half-life.

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