Analysis of a rock sample that it contains 6.25% of its original uranium-235. How old is the rock? How do you know?

The age of the rock = 2800.6 million years = 2.8 billion years.

A simple method of analysis similar to Carbon dating is used to obtain the required age of the rock. Radioactive substances decay according to first order reaction kinetics. So, plugging all the required parameters into the general equation for amount of substance left in a first order decay gives us the age of the rock.

Explanation:

Half life of Uranium-235 = 700 million years (from literature)

The decay of radioactive substances follow first order reaction kinetics.

The general equation is given as

A(t) = A₀ e⁻ᵏᵗ

A(t) = Amount of radioactive substance left after a particular time = 6.25%

A₀ = initial amount of radioactive substance = 100%

t = time that has passed since the beginning = age of the rock = ?

k = decay constant

The decay constant is related to the half life (T) through the relation,

k = (In 2)/T

k = (0.693/700) = 0.00099 /million years

A(t) = A₀ e⁻ᵏᵗ

6.25 = 100 e⁻ᵏᵗ

0.0625 = e⁻ᵏᵗ

In e⁻ᵏᵗ = In 0.0625 = -2.7726

-kt = - 2.7726

t = (2.7726/0.00099) = 2800.6 million years

t = 2.8 billion years.

Hope this Helps!!!