What Fraction Of A 15o Sample Decays In 10 Min, Radioactive elements are known for their unstable nature, and they tend to decay over time. One such, General, what-fraction-of-a-15o-sample-decays-in-10-min, JPOSE
Radioactive elements are known for their unstable nature, and they tend to decay over time. One such element is Oxygen-15, which is commonly used in medical imaging procedures. 15O has a half-life of 2 minutes, which means that half of the initial sample will decay in that time.
So, what fraction of a 15O sample decays in 10 minutes? To answer this question, we need to use the formula for radioactive decay:
N(t) = N0 e^(-λt)
Where N(t) is the amount of the substance remaining after time t, N0 is the initial amount, λ is the decay constant, and e is the mathematical constant approximately equal to 2.718.
In this case, we know that the initial amount of the sample is 1 (since we're dealing with fractions), the decay constant λ is ln(2)/t1/2 (where t1/2 is the half-life), and the time t is 10 minutes.
Plugging these values into the formula, we get:
N(10) = 1 * e^(-ln(2)/2 * 10)
N(10) = 1 * e^(-ln(2) * 5)
N(10) ≈ 0.080
Therefore, about 0.080 of the initial sample will remain after 10 minutes, and the remaining fraction (0.920) will have decayed.
In conclusion, knowing the half-life of a radioactive substance allows us to calculate how much of the sample will remain after a certain amount of time. In the case of Oxygen-15, about 8% of the initial sample will remain after 10 minutes, and the remaining 92% will have decayed.