A sample initially contains 3200 radioactive nuclei. Find the number of nuclei that decay between the end of the second half-life and the end of the fifth half-life.
Physics · Nuclear physics · radioactivity and law of decay
JEE Mains NEET JEE Advanced

Question

A sample initially contains 3200 radioactive nuclei. Find the number of nuclei that decay between the end of the second half-life and the end of the fifth half-life.

G1 Physics · Accepted Answer

After two half-lives, the remaining nuclei are N₂ = 3200×(1 ÷ 2²) = 3200 ÷ 4 = 800. After five half-lives: N₅ = 3200×(1 ÷ 2⁵) = 3200 ÷ 32 = 100. The number that decay between those two instants is 800−100 = 700. Hence N = 700.