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.

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.