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The mass at time t of a radioactive substance is m(t)=m(0)ekt, where m(0) is the initial mass and k=−0.000135. The mean life M of an atom in this substance is M=−k∫∞0tektdt=

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Answer:

7407.4 units

Explanation:

m(t) = m(0) e^kt

Here, k = - 0.000135

So, the above equation becomes

m(t) = m(0) e^(-0.000135 t)

Compare with the standard equation of radioactivity

m(t) = m(0) e^-λt

Where, λ be the decay constant

So. λ = 0.000135

The relation between the decay constant and the mean life is

ζ = 1 / λ

Where, ζ is the mean life

So, ζ = 1 / 0.000135 = 7407.4 units

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