Question
Download Solution PDFThe relation between half life (T) and decay constant (λ) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
- As per radioactive decay law, the total number of nuclei of radioactive compounds after radioactive decay in the sample is given by given equation
where N is the number of nuclei of radioactive compounds after radioactive decay, N0 is the number of nuclei of radioactive compounds initially, λ is the decay constant and t is the time of radioactive decay.
- Half-Life: Half-life is the time required for a radioactive substance to reduce to its half initial value.
CALCULATION:
- From the definition of half-life, radioactive decay in time T (half-life) will be half of its initial value
N = N0 / 2
so at time t = T, no of nuclei is N = N0 / 2
where N0 is the initial number of nuclei.
From radioactive decay law:
Taking log on both the sides
⇒ λ T = loge 2
- So the correct answer will be option 3.
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