Question:
The half-life of a radioactive substance is 10 days. The decay constant is
The half-life of a radioactive substance is 10 days. The decay constant is
Show Hint
Remember that the decay constant can be calculated using the formula \( \lambda = \frac{\ln 2}{t_{1/2}} \).
Updated On: Jun 3, 2026
- $0.0693 \text{ / day}$
- $0.693 \text{ / day}$
- $6.93 \text{ / day}$
- $0.00693 \text{ / day}$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The relationship between the half-life of a radioactive substance and its decay constant is given by the formula: \[t_{1/2} = \frac{\ln 2}{\lambda}\] where \( t_{1/2} \) is the half-life, and \( \lambda \) is the decay constant.
Step 2: Meaning
The half-life of a radioactive substance is the time it takes for half of the substance to decay. The decay constant represents the probability per unit time that an atom will decay.
Step 3: Analysis
Given the half-life \( t_{1/2} = 10 \) days, we can use the formula to find the decay constant \( \lambda \): \[\lambda = \frac{\ln 2}{t_{1/2}} = \frac{\ln 2}{10}\] We know that: \[\ln 2 \approx 0.693\] Thus, \[\lambda = \frac{0.693}{10} = 0.0693 \text{ / day}\] This matches option A.
Step 4: Conclusion
The decay constant for the radioactive substance with a half-life of 10 days is \( 0.0693 \text{ / day} \).
Final Answer: (A)
The relationship between the half-life of a radioactive substance and its decay constant is given by the formula: \[t_{1/2} = \frac{\ln 2}{\lambda}\] where \( t_{1/2} \) is the half-life, and \( \lambda \) is the decay constant.
Step 2: Meaning
The half-life of a radioactive substance is the time it takes for half of the substance to decay. The decay constant represents the probability per unit time that an atom will decay.
Step 3: Analysis
Given the half-life \( t_{1/2} = 10 \) days, we can use the formula to find the decay constant \( \lambda \): \[\lambda = \frac{\ln 2}{t_{1/2}} = \frac{\ln 2}{10}\] We know that: \[\ln 2 \approx 0.693\] Thus, \[\lambda = \frac{0.693}{10} = 0.0693 \text{ / day}\] This matches option A.
Step 4: Conclusion
The decay constant for the radioactive substance with a half-life of 10 days is \( 0.0693 \text{ / day} \).
Final Answer: (A)
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