A 2.00 g sample of the radioisotope phosphorus-32 is found to contain 0.250 g of phosphorus-32 after 42.0 days.

Calculate the half-life of this isotope.

Question

A 2.00 g sample of the radioisotope phosphorus-32 is found to contain 0.250 g of phosphorus-32 after 42.0 days.

Calculate the half-life of this isotope.

| General Chemistry 2

Accepted Answer

Radioactive decay is a first-order process:

ln $(\frac{N}{N_{0}})$ = - kt and t_1/2 = $\frac{\ln 2}{k}$

⇒ t_1/2 = -

\frac{\ln 2 \times t}{\ln (\frac{N}{N_{0}})}

⇒ t_1/2 = -

\frac{\ln 2 \times 42}{\ln (\frac{0.250}{2.00})}

= 14.0 days

Radioactive decay - 1 | Chemical Kinetics: Rate Laws