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NEET · Chemistry · STD 12 - 3. Chemical kinetics
The rate of radioactive disintegration at an instant for a radioactive sample of half life \(2.2 \times 10^{9}\; \mathrm{s}\) is \(10^{10} \;\mathrm{s}^{-1} .\) The number of radioactive atoms in that sample at that instant is
- A \(3.17 \times 10^{20}\)
- B \(3.17 \times 10^{17}\)
- C \(3.17 \times 10^{18}\)
- D \(3.17 \times 10^{19}\)
Answer & Solution
Correct Answer
(D) \(3.17 \times 10^{19}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{T}_{1 / 2}=2.2 \times 10^{9} \mathrm{s}, \mathrm{R}=10^{10} \mathrm{s}^{-1}, \mathrm{R}=\mathrm{N} \lambda\) \(\mathrm{N}=\frac{\mathrm{R}}{\lambda}=\frac{\mathrm{R}}{0.693} \mathrm{T}_{1 / 2}=\frac{10^{10} \times 2.2 \times 10^{9}}{0.693}\)\(=3.17 \times 10^{19}\; atoms\)
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