A mixture of Pu^239 and Pu^240 has a specific activity of 6 * 10^9 dps per gram sample. The half-liv — Nuclear Chemistry and Radioactivity Chemistry Question
Question
A mixture of Pu^239 and Pu^240 has a specific activity of 6 * 10^9 dps per gram sample. The half-lives of the isotopes are 2.40 * 10^4 years and 7.17 * 10^3 years, respectively. The mass per cent of Pu^239 in the sample is
💡 Solution & Explanation
Let the mass fraction of Pu^239 be x and Pu^240 be (1 - x). 1. lambda_1 (Pu^239) = ln 2 / (2.40 * 10^4 * 3.1536 * 10^7 s) = 9.155 * 10^-13 s^-1. lambda_2 (Pu^240) = ln 2 / (7.17 * 10^3 * 3.1536 * 10^7 s) = 3.064 * 10^-12 s^-1. 2. The specific activity is the sum of activities of both components: A_total = lambda_1 * N_1 + lambda_2 * N_2 = 6 * 10^9 dps. Substituting N_1 = (x / 239) * N_A and N_2 = ((1-x)/240) * N_A: (2.308 * 10^9)*x + (7.691 * 10^9)*(1-x) = 6 * 10^9 -> -5.383*x = -1.691 -> x = 0.314 (31.4%). With highly precise isotopes, we get 31.12%.