Question
A sample of a radioactive isotope has an initial activity of 400 decays per second. Calculate the activity of the sample after 30 minutes, given the isotope's half-life is 20 minutes.
A sample of a radioactive isotope has an initial activity of 400 decays per second. Calculate the activity of the sample after 30 minutes, given the isotope's half-life is 20 minutes.
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Koala Tutor
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The activity of a sample of radioactive isotopes can be calculated using the formula:
A = A₀ * (1/2)^(t / T)
Where:
A = final activity
A₀ = initial activity
t = time elapsed
T = half-life
Plugging in the given values:
A = 400 * (1/2)^(30 / 20)
Simplifying the exponent:
A = 400 * (1/2)^1.5
Calculating the exponent:
A = 400 * 0.3536
A ≈ 141.44
The activity of the sample after 30 minutes is approximately 141.44 decays per second.
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