The half life of U-238 against alpha decay is 4.5 x 10^9 years, find the activity of 1 kg of U-238:
Correct answer: B. 3.34 x 10^-4 Ci
- A. 2.4 x 10^-4 Ci
- B. 3.34 x 10^-4 Ci
- C. 4.34 x 10^-4 Ci
- D. 2.4 x 10^-5 Ci
Explanation
The number of atoms in 1kg of U-238 (N) = moles x Avagadro's constant = (mass/Mr) x Avagadro's constant = (1000/238) x 6.02x1023 = 2.529x1024Half-life = 4.5x109 yearsConverting this into seconds:(4.5x109) x (3.26x107)1.42x1017sA = λNWhere A is activity in Bq and λ is decay constantλ = 0.693/half-lifeA = (0.693/half-life)NA = (0693/1.42x1017)(2.529x1024)A = 1.234x107 BqConverting Bq to Ci1 Ci = 3.7x1010 BqA = 1.234x107/ 3.7x1010A = 3.34 x 10-4 Ci
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