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=

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