Question

The decay of cesium-135 is first order with a half life is 3.0 million years. How much of 1.1378 g sample would remain after 8.47 million years?

Answer 1

Given the half life of the first order reaction, t_1/2 = 3.0 million years

Hence rate constant, k = 0.693 / t_1/2  = 0.693 / 3.0 million years = 0.231 (million year)^-1

t = 8.47 million years

The amount of substance remained after  8.47 million years can be calculated from the following relation

t = (2.303 / k) x log(N₀ / N)

=> 8.47 million years = (2.303 / 0.231 (million year)^-1) x log(1.1378 g / N)

=> log(1.1378 / N) = 0.8496

=> 1.1378 g / N = 7.07

=> N = 1.1378 g / 7.07 = 0.161 g (answer)