A radio-active elements has half-life of 15 years. What is the fraction that will decay in 30 years?

Step-by-step solution

Given, half-life, T_ 1 / 2 =15 years Time, t=30 years Number of half-life, n= t T = 30 15 =2 The number of nuclei left undecayed in 30 years or 2 half-lives is aligned N=N₀ ( 1 2 )^ n N N₀ &= ( 1 2 )²= 1 4 Fraction of decayed element &= (1- N N₀ )=1- 1 4 &= 3 4 or 0.75 aligned