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JIPMER 2016
Exam
JIPMER
Year
2016
Subject
Chemistry
Chapter
Chemical Kinetics

JIPMER 2016 · Chemistry · Chemical Kinetics

At radioactive equilibrium, the ratio between two atoms of...

At radioactive equilibrium, the ratio between two atoms of radioactive elements AA and BB is 3.1×109:13.1 \times 10^9: 1. If the half-life period of AA is 2×10102 \times 10^{10} yrs, then the half-life of BB is

Options

  1. A9.54 yrs
  2. B2.14 yrs
  3. C3.29 yrs
  4. D6.45 yrs

Correct answer

D. 6.45 yrs

Step-by-step solution

At radioactive equilibrium, A⟶BA \longrightarrow BNANB=KBKA=t1/2At1/2B∴3.1×1091=2×1010t1/2B and, t1/2B=6.45yrs.\begin{aligned} \frac{N_A}{N_B} & =\frac{K_B}{K_A}=\frac{t_{1 / 2 A}}{t_{1 / 2 B}} \\ \therefore \quad \frac{3.1 \times 10^9}{1} & =\frac{2 \times 10^{10}}{t_{1 / 2 B}} \text{ and, } t_{1 / 2 B}=6.45 \mathrm{yrs} .\end{aligned}$$
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