Question

The half-life of cesium-137, released as a result of the Fukushima Daiichi nuclear disaster, is 30.2 years. Determine the number of years it would take for the amount of cesium-137 to decrease to 7 % of the original amount released in the disaster. Round your answer to the nearest number of years.

Answer 1

Radioactive disintegration is the first order disintegration process.

The half-life of cesium-137 = 30.2 years

The relation between the half-life period(t_1/2) and the decay constant() is as follows:

Decay constant() = 0.693 / half-life period(t_1/2)

Substitute 30.2 years for half-life period(t_1/2) and determine the decay constant as follows:

Decay constant() = 0.693 / 30.2 years

Decay constant() = 0.023 year^-1

The first order integrated rate equation is as follows:

Initial amount of cesium-137 (N₀)= 100 %

Amounto of cesium-137 remaining after time t (N_t) = 7 %

ln[N_t/N₀] = -kt

Rearrange the formula for t as follows:

t = (-1/k){ln[N_t/N₀]}

Substitute 0.023 year^-1 for k, 7 for N_t and 100 for N₀, Determine the time required as follows:

t = (-1/0.023 year^-1){ln[7/100]}

t = 116 years

Thus, the time required for the amount of cesium-137 to decrease to 7% of the original amount is 120 years. [2 S.F].