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KVPY2017ChemistryChemical Kinetics

²²⁷ Ac has a half-life of 22 years with respect to radioactive decay . The decay follows two parallel paths : ²²⁷ Ac ²²⁷ Th and ²²⁷ Ac ²²³ Fr . If the percentage of the two daughter nuclides are 2.0 and 98.0 , respectively, the decay constant (in year ⁻¹ ) for ²²⁷ Ac ²²⁷ Th path is closest to

Options

  1. A6.3 10⁻²
  2. B6.3 10⁻³
  3. C6.3 10⁻¹
  4. D6.3 10⁻⁴

Correct answer

D. 6.3 10⁻⁴

Step-by-step solution

Ac ^ R ₁ / R ₂ Ac % Th = R ₁ R _ T = 2 100 % Ac = R ₂ R _ T = 98 100 R ₁ R ₂ = 2 98 R _ T = R ₁+ R ₂ 0.693 22 = R ₁+ 98 2 R ₁ R ₁= 6 . 3 1 0 ⁻⁴

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