Question

A storage tank contains a liquid radioactive element with a half-life of 96 years. It will be relatively safe for the contents to leak from the tank when 0.02% of the

radioactive element remains. How long must the tank remain intact for this storage procedure to be safe?
The tank must remain intact for lears.
(Round the base of the exponential function to four decimal places. Then round the final answer to the nearest year as needed.)

Answer 1

t = 1180 years

Explanation:

We will solve this using the radioactive decay formula which is;

A = A_o × 2^(-t/h)

Where;

A = Amount of liquid remaining after time (t)

A_o = initial amount of liquid at initial time

t = time of decay

h = half-life of the liquid

We have;

A_o = 1(we assume it is 100% which is 1)

A = 0.02% = 0.0002

h = 96 years

Thus;

0.0002 = 1 × 2^(-t/96)

0.0002 = 2^(-t/96)

(-t/96)log 2 = log 0.0002

(-t/96) = (log 0.0002)/log 2

(-t/96) = -12.2877

t = 96 × 12.2877 (negative has canceled out)

t = 1179.6192

To the nearest year gives;

t = 1180 years