The half-life of Radium-223 is 11.43 years. What is the annual decay rate? Express the result to four decimal places.
(1/2)^(1/11.43) = 0.94116
so, it loses 5.884% per year
To determine the annual decay rate of Radium-223, we need to divide the half-life by the natural logarithm of 2.
The natural logarithm of 2, denoted as ln(2), is approximately 0.6931.
So, the annual decay rate (R) can be calculated using the formula:
R = (ln(2)) / (half-life)
In this case, the half-life of Radium-223 is given as 11.43 years. Plugging in the values:
R = (0.6931) / (11.43)
Evaluating the expression:
R ≈ 0.06064
Therefore, the annual decay rate of Radium-223 is approximately 0.0606 (rounded to four decimal places).
To find the annual decay rate of Radium-223, we need to calculate the fraction of the substance that decays per year.
The decay rate can be calculated using the formula:
decay rate = 1 / (half-life)
Let's calculate it:
decay rate = 1 / 11.43
≈ 0.0874
Therefore, the annual decay rate of Radium-223 is approximately 0.0874.