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The half-life of a radioactive substance is 2 seconds. Calculate the decay constant.

Physics
NECO 2000

The half-life of a radioactive substance is 2 seconds. Calculate the decay constant.

  • A. 2.890 s-1
  • B. 1 .445 s-1
  • C. 0.576 s-1
  • D. 0.347s-1
  • E. 0.152 s-1
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Correct Answer: Option D
Explanation

\(T_{\frac{1}{2}} = \frac{\ln 2}{\lambda}\)

where \(T_{\frac{1}{2}}\) = half-life of element; \(\lambda\) = decay constant.

= \(\frac{0.693}{\lambda}\)

\(\therefore 2 = \frac{0.693}{\lambda}\)

\(\lambda = \frac{0.693}{2}\)

= 0.3465 s\(^{-1}\)

\(\approxeq\) 0.347 s\(^{-1}\)


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