JEE Mains · Physics · STD 12 - 13. Nuclei
If a radioactive element having half-life of \(30\,min\) is undergoing beta decay, the fraction of radioactive element remains undecayed after \(90\,min\). will be :
- A \(\frac{1}{8}\)
- B \(\frac{1}{16}\)
- C \(\frac{1}{4}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{8}\)
Step-by-step Solution
Detailed explanation
\(\frac{ N }{ N _0}=\left(\frac{1}{2}\right)^{ t / t \frac{1}{2}}=\left(\frac{1}{2}\right)^{\frac{90}{30}}\) \(\frac{ N }{ N _0}=\left(\frac{1}{2}\right)^3=\frac{1}{8}\)
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