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

a rain shadow is a dry region of land on the side that is protected against the prevailing winds of a mountain range. the prevailing winds are the winds that occur most of the time in a particular place of the earth

prevailing winds carry air toward the mountain range. as the air rises up over a mountain range, the air cools, water vapor condenses, and clouds form. on this side of the mountains, called the windward side, precipitation falls in the form of  rain  or snow. this dry air produces a  rain shadow.