If the decay constant for element X is 6.931 yr^{-1}, what is its half-life?

• A. 10 yr
• B. 0.1 yr
• C. 100 yr
• D. 1 yr

Answer: (B)

Verified step by step guidance

1. Recall the relationship between the decay constant (\lambda) and the half-life (t_{1\/2}) of a radioactive element, which is given by the formula: \[ t_{1\/2} = \frac{\ln(2)}{\lambda} \]
2. Identify the given decay constant \( \lambda = 6.931 \; \text{yr}^{-1} \).
3. Substitute the given decay constant into the half-life formula: \[ t_{1\/2} = \frac{\ln(2)}{6.931} \]
4. Calculate \( \ln(2) \), which is approximately 0.6931, and then divide by the decay constant to find the half-life in years.
5. Interpret the result to determine which of the provided options (10 yr, 0.1 yr, 100 yr, 1 yr) matches the calculated half-life.