QuestionMay 6, 2025

The decay constant for a particular radioactive element is .026 when time is measured in years. Find the half-life of the element. The half-life is square years. (Round to one decimal place as needed.)

The decay constant for a particular radioactive element is .026 when time is measured in years. Find the half-life of the element. The half-life is square years. (Round to one decimal place as needed.)
The decay constant for a particular radioactive element is .026 when time is measured in years. Find the half-life of the element. The half-life is square years. (Round to one decimal place as needed.)

Solution
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Answer

The half-life is 26.7 years. Explanation 1. Use the half-life formula The formula for half-life is T_{1/2} = \frac{\ln(2)}{\lambda}, where \lambda is the decay constant. 2. Substitute the given decay constant \lambda = 0.026. Substituting into the formula: T_{1/2} = \frac{\ln(2)}{0.026}. 3. Perform the calculation \ln(2) \approx 0.693, so: T_{1/2} = \frac{0.693}{0.026} \approx 26.7 years.

Explanation

1. Use the half-life formula<br /> The formula for half-life is $T_{1/2} = \frac{\ln(2)}{\lambda}$, where $\lambda$ is the decay constant.<br /><br />2. Substitute the given decay constant<br /> $\lambda = 0.026$. Substituting into the formula: <br />$T_{1/2} = \frac{\ln(2)}{0.026}$.<br /><br />3. Perform the calculation<br /> $\ln(2) \approx 0.693$, so: <br />$T_{1/2} = \frac{0.693}{0.026} \approx 26.7$ years.
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