The half-life of the first-order decay of radioac- . 14C . b l:Ive 1s a out 5720 years. Calculate the rate constant for the reaction. (b) The natural abundance of 14C isotope is 1.1 x I 0-13 mol % in living matter. Radiochemical analysis of an object obtained in an archeological excavation shows that the 14 C isotope content is 0.89 x 10-14 mol %. Calculate the age of the object. State any assumptions.

a. Rate constant: 1.2118x10⁻⁴ yrs⁻¹

b. The age of the object is 20750 years

Explanation:

a. We can solve the rate constant in an isotope decay by using Half-Life, as follows:

K = Ln 2 / Half-life

K = ln 2 / 5720 years =

b. The general equation of isotope decay is:

Ln [A] = -kt + Ln [A]₀

Where [A] is concentration of the isotope after time t,

k is rate constant

and [A]₀ initial concentration of the isotope.

Computing the values of the problem:

Ln [0.89x10⁻¹⁴] = -1.2118x10⁻⁴ yrs⁻¹t + Ln [1.1x10⁻¹³]

-2.5144 = -1.2118x10⁻⁴ yrs⁻¹t

20750 years = t

The age of the object is 20750 years

d.) the average kinetic energy of the gas particles is greater in container b because its particles move faster.