KCET · Physics · Nuclear Physics
A radioactive substance emits 100 beta particles in the first \(2 \mathrm{~s}\) and 50 beta particles in the next \(2 \mathrm{~s}\). The mean life of the sample is
- A \(4 \mathrm{~s}\)
- B \(2 \mathrm{~s}\)
- C \(\frac{2}{0.693} \mathrm{~s}\)
- D \(2 \times 0.693 \mathrm{~s}\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{0.693} \mathrm{~s}\)
Step-by-step Solution
Detailed explanation
Given, In 1st two seconds \(100 \beta\) particles and in next two seconds \(50 \beta\) particles are emitted
\(\begin{array}{ll}
\therefore & T_{1 / 2}=2 \mathrm{~s} \\
\text { Hence, } & T_{m}=\frac{T_{1 / 2}}{0.693}=\frac{2}{0.693}
\end{array}\)
\(\begin{array}{ll}
\therefore & T_{1 / 2}=2 \mathrm{~s} \\
\text { Hence, } & T_{m}=\frac{T_{1 / 2}}{0.693}=\frac{2}{0.693}
\end{array}\)
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