Question

Radioactive elements decay via first-order kinetics. consider a certain type of nucleus that has a rate constant of 2.4 × 10–2 h–1. a sample contains 6.5 × 108 radioactive nuclides. calculate the time required for 59% of the nuclides to decompose.

Answer 1

Answer:

37.15 h.

Explanation:

• The decay of radioactive elements obeys first-order kinetics.

• For first-order reaction: kt = lna/(a-x).

where, k is the rate constant of the reaction (k = 2.4 x 10⁻² h⁻¹).

t is the time of the reaction (t = ??? day).

a is the initial concentration of nuclides (a = 100 %).

(a-x) is the remaining concentration of nuclides (a - x = 100% - 59% = 41.0 %).

∴ kt = lna/(a-x)

(2.4 x 10⁻² h⁻¹)(t) = ln(100.0%)/(41.0%).

(2.4 x 10⁻² h⁻¹)(t) = 0.8916.

∴ t = (0.8916)/(2.4 x 10⁻² h⁻¹) = 37.15 h.