After 42 days, a 2.0 g sample of phosphorous-32 contains only 0.25 g of the isotope. What is the half-life of phosphorus-32?

Half life of phosphorous-32 = 14 days

Explanation:

Given data:

Total mass of phosphorous-32 = 2.0 g

After 42 days mass left = 0.25 g

Half life of phosphorous-32 = ?

Solution:

First of all we will calculate the number of half lives passed.

At time zero = 2.0 g

At first half life = 2.0 g/2 = 1.0 g

At 2nd half life = 1.0 g/2 = 0.5 g

At 3rd half life = 0.5 g/2 = 0.25 g

Half life:

Half life = T elapsed / half lives

Half life = 42 days/ 3

Half life = 14 days