The relation between the decay constant λ and the half-life T1/2 is
Correct answer: B. T1/2 = 0.693/λ
- A. λ = T1/2
- B. T1/2 = 0.693/λ
- C. λ = T1/2/0.693
- D. λ = T1/2 x 0.693
Explanation
The relationship between the decay constant (λ) and the half-life (T₁/₂) is given by the following equation:T₁/₂ = ln(2) / λ Where:T₁/₂ is the half-life λ is the decay constantln(2) is the natural logarithm of 2, which is approximately 0.693 This equation can also be written as:T₁/₂ ≈ 0.693 / λ In simpler terms, the half-life is inversely proportional to the decay constant. A larger decay constant means a shorter half-life, and vice versa.The decay constant represents the probability of decay of a nucleus per unit time. The half-life is the time it takes for half of the radioactive nuclei in a sample to decay.
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About Half-life and Rate of Decay
Half-life is the time required for half the unstable nuclei in a sample to decay, and it remains constant for a particular radioactive nuclide. Questions use the exponential decay law, decay constant, activity, remaining quantity and mean life. Radioactive decay is random for individual nuclei but predictable for large samples.
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