The half-life of cesium-137 is 30 years. Suppose we have a 200-mg sample. (a) Find the mass that remains after t years.

Given:

Half life (t^ 1/2) : 30 years

A0 (initial mass of the substance) : 200 mg.

Now we know that

A = A0 / [2 ^ (t/√t) ]

Where A is the mass that remains after t years.

A0 is the initial mass

t is the time

t^1/2 is the half life

Substituting the given values in the above equation we get

A = [200 / 2^ (t/30) ] mg

Thus the mass remaining after t years is [200 / 2^ (t/30) ] mg