How long will it take a piece of strontium-90 (produced in a nuclear test blast) weighing exactly 1000.0 g to be reduced to 15.625 g? The half-life of strontium 90 is 28.8 years,

Time taken 172.8 years

Explanation:

Given data:

Total amount of strontium-90 = 1000.0 g

Amount left = 15.625 g

Half life of strontium = 28.8 years

Time taken = ?

Solution:

Number of half lives:

At time zero = 1000.0 g

At first half life = 1000.0g/2 = 500 g

At second half life = 500 g/2 = 250 g

At third half life = 250 g/ 2 = 125 g

At 4th half life = 125 g/ 2= 62.5 g

At 5th half life = 62.5 g/2 = 31.25 g

At 6th half life = 31.25 g / 2 = 15.625 g

Time taken:

Time taken = number of half lives × half life

Time taken = 6×28.8 years

Time taken = 172.8 years