A sample of a radioactive element that contains 1.0 x 103 nuclei decays to 6.2 x 101 nuclei in 10. Minutes, What is its specific decay constant?

621000=e−λt2.78=λtλ=2.78t=2.7810 min−1 λ=0.28 min−1

A sample of a radioactive element that contains 1.0 x 103 nuclei decays to 6.2 x 101 nuclei in 10. Minutes, What is its specific decay constant?

621000=e−λt2.78=λtλ=2.78t=2.7810 min−1 λ=0.28 min−1

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A sample of a radioactive element that contains 1.0 x 10³ nuclei decays to 6.2 x 10¹ nuclei in 10. Minutes, What is its specific decay constant?

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0.28 min^-1

1.2 min^-1

6.2 min^-1

0.062 min^-1

answer is C.

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Detailed Solution

$\frac{62}{1000} = e^{- λ t}$

$2.78 = λ t$

$λ = \frac{2.78}{t} = \frac{2.78}{10} \min^{- 1}$

$λ = 0.28 \min^{- 1}$

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A sample of a radioactive element that contains 1.0 x 103 nuclei decays to 6.2 x 101 nuclei in 10. Minutes, What is its specific decay constant?

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A sample of a radioactive element that contains 1.0 x 10³ nuclei decays to 6.2 x 10¹ nuclei in 10. Minutes, What is its specific decay constant?