Question:
the half life of U 238; 92 undergoing alpha decay is 4.5x10^9 yrs. determine the activity of 10g of sample of U 238;92. given that 1g of U 238;92 contains 25.3x10^20 atoms
Answer:
- Half life of U92238 is 4.5 * 109 years
- Converting the same into seconds, we get 4.5 * 109 years * 365.25 days * 24 hours * 60 min * 60 sec = 1.42009 * 1017 sec
- Mean life Ʈ = Half life / 0.6931 = 1. 42009 * 1017 / 0.6931 = 2.0489 * 1017 sec
- The decay rate λ = 1/ Ʈ = 1/ 0489 * 1017 per sec = 0.488 * 10-17 per sec
- Mass of 10 g decay = λ * 10 = 488 * 10-17 * 10 = 4.88 * 10-17 g per sec
- Decay constant in g/sec to be converted into atoms per sec by using the atomic mass and the avagrado number 6.022 * 1023 atoms / mole
- Hence, 4.88 * 10-17 g per sec * 25.3 * 10 23 as given in the sum which is 1,23,464 atoms / sec
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