Half-life refers to the time taken by a radioactive material to decay by half of the original mass.
In this case, the half-life of element X is 10 years, which means it takes 10 years for a given mass of the element to decay by half of its original mass.
To calculate the amount that remained after decay we use;
Remaining mass = Original mass × (1/2)^n, where n is the number of half-lives
Number of half-lives = Time for the decay ÷ Half-life
= 40 years ÷ 10 years
= 4
Therefore;
Remaining mass = 300 g × (1/2)⁴
= 300 g × 1/16
= 18.75 g
Hence, a mass of 300 g of an element X decays to 18.75 g after 40 years.
