Q175 / 180 · KCET 2016 · Physics
A radio-active sample of half-life \( 10 \) days contains \( 1000 \times \) nuclei. Number of original nuclei
present after \( 5 \) days is
present after \( 5 \) days is
- Correct answerA\( 707 x \)
- B\( 750 x \)
- C\( 500 x \)
- D\( 250 x \)
Solution
Given, half-life, \( T_{1 / 2}=10 \) days; \( N_{0}=1000 x ; t=5 \) days
Now, \( t=\frac{1}{2} T_{\frac{1}{2}}=n T_{\frac{1}{2}} \)
\( \Rightarrow n=\frac{1}{2} \) \( \Rightarrow N=\frac{N_{0}}{2^{n}}=\frac{1000 x}{2^{1 / 2}}=\frac{1000 x}{1.414}=707.21 x \)
Therefore, number of original nuclei present after \( 5 \) days is \( 707.21 x \sim 707 x \)
Now, \( t=\frac{1}{2} T_{\frac{1}{2}}=n T_{\frac{1}{2}} \)
\( \Rightarrow n=\frac{1}{2} \) \( \Rightarrow N=\frac{N_{0}}{2^{n}}=\frac{1000 x}{2^{1 / 2}}=\frac{1000 x}{1.414}=707.21 x \)
Therefore, number of original nuclei present after \( 5 \) days is \( 707.21 x \sim 707 x \)
Hence, the correct answer is option: 'A'.