CUET · CHEMISTRY · PYQ PAPER 2023
The half life of decaying \({ }^{14} C\) is 6000 years approximately. How much time is needed to decaying \(80 \%\) of \({ }^{14} C ?[\log 5=0.6990]\)
- A 3937.6 years
- B 250.0 years
- C 13937.6 years
- D 23937.6 years
Answer & Solution
Correct Answer
(D) 23937.6 years
Step-by-step Solution
Detailed explanation
\( \frac{N}{N_0} = (0.20) \) \( t = T_{1/2} \frac{\log(N_0/N)}{\log 2} \) \( t = 6000 \text{ years} \times \frac{\log(1/0.2)}{\log 2} \) \( t = 6000 \text{ years} \times \frac{\log 5}{\log 2} \) \( t = 6000 \text{ years} \times \frac{0.6990}{0.3010} \)…
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