Question

If 18 g of a radioactive substance are present initially and 8 yr later, only 9 g remain, how much substance will be present after 12 yr?

Answer 1

Step 1: we have to obtain the number of grams lost by the radioactive substance every year.

For an 18g radioactive substance,

If 9g remains after 8years, this implies that:

`(9)/(8)\text{ grams = 1.125g of the radioactive substance is lost every year}`

The number of years left to complete 12years after the 8years period is 4 years.

Since 1.125g of the radioactive substance is lost every year, this implies that:

`1.125g\text{ x 4 = 4.5g will be lost for the remaining 4years period}`

Therefore, the total loss for the 12 years period is :

`9g+4.5g\text{ = 13.5g}`

The amount of substance that will be left after 12years is:

`18g-13.5g=4.500g`

Hence, after 12years, 4.500g of the radioactive substance will be left.