Question

The half-life of a radioactive isotope is 3 h. If the initial mass of the isotope was 300 g, the mass which remained undecayed after 18 h would be

• A. 4.68 g
• B. 2.34g
• C. 1.17 g
• D. 9.36 g

Answer 1

Answer: (A)

4.68 g

Answer 2

Given, Half-life $(t_{1/2})$ = 3h Initial mass {N0) = 300 g Total time (T) = 18 h Mass left {N) = ? We know that, $\, \, \, \, \, \, \, \, \, \, \, \, \, \, \frac{N}{N_0}=\Bigg(\frac{1}{2}\Bigg)^n$ where, n = number of half-lives $\, \, \, \, \, \, \, \, \, \, \, \, \, \, n=\frac{Total time}{Half-life }=-\frac{18}{3}=6$ So, $\, \, \, \, \, \, \, \, \, \, \, \frac{N}{300}=\Bigg(\frac{1}{2}\Bigg)^6$ So, $\, \, \, \, \, \, \, \, \, \, \, \frac{1}{300}=\frac{1}{64}$ $\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, N=\frac{300}{64}=4.68g$