SATHEE: Modern Physics 3 Question 8

Modern Physics 3 Question 8

8. A radioactive sample $S_{1}$ having an activity of $5 μ C i$ has twice the number of nuclei as another sample $S_{2}$ which has an activity of $10 μ C i$ . The half lives of $S_{1}$ and $S_{2}$ can be

(a) $20 y r$ and $5 y r$ , respectively

$(2008, 3 M)$

(b) $20 y r$ and $10 y r$ , respectively

(d) 5 yr each

Show Answer

Solution:

Activity of $S_{1} = \frac{1}{2}$ (activity of $S_{2}$ )

or $λ_{1} N_{1} = \frac{1}{2} (λ_{2} N_{2})$

or $\frac{λ_{1}}{λ_{2}} = \frac{N_{2}}{2 N_{1}}$

or $\frac{T_{1}}{T_{2}} = \frac{2 N_{1}}{N_{2}} T =$ half - life $= \frac{\ln 2}{λ}$

Given $N_{1} = 2 N_{2}$

$∴ \frac{T_{1}}{T_{2}} = 4$

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Modern Physics 3 Question 8

8. A radioactive sample S1 having an activity of 5μCi has twice the number of nuclei as another sample S2 which has an activity of 10μCi. The half lives of S1 and S2 can be

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8. A radioactive sample $S_{1}$ having an activity of $5 μ C i$ has twice the number of nuclei as another sample $S_{2}$ which has an activity of $10 μ C i$ . The half lives of $S_{1}$ and $S_{2}$ can be