The half life of a radioactive substance is $20$ minutes. The approximate time interval $(t_2 -t_1)$ between the time $t_2$ when $3/4$ of it has decayed and time $t_1$ when $1/4$ of it had decayed is
The half life of a radioactive substance is $20$ minutes. The approximate time interval $(t_2 -t_1)$ between the time $t_2$ when $3/4$ of it has decayed and time $t_1$ when $1/4$ of it had decayed is
- A
$\frac{{20}}{{\ln 2}}\min$
- B
$\frac{{20\ln 3}}{{\ln 2}}\min$
- C
$20$ $min$
- D
$20\ln 2\min$
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The activity $R$ of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows:
$t(h)$
$0$
$1$
$2$
$3$
$4$
$R(MBq)$
$100$
$35.36$
$12.51$
$4.42$
$1.56$
$(i)$ Plot the graph of $R$ versus $t$ and calculate half-life from the graph.
$(ii)$ Plot the graph of $\ln \left( {\frac{R}{{{R_0}}}} \right) \to t$ versus $t$ and obtain the value of half-life from the graph.
The activity $R$ of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows:
| $t(h)$ | $0$ | $1$ | $2$ | $3$ | $4$ |
| $R(MBq)$ | $100$ | $35.36$ | $12.51$ | $4.42$ | $1.56$ |
$(i)$ Plot the graph of $R$ versus $t$ and calculate half-life from the graph.
$(ii)$ Plot the graph of $\ln \left( {\frac{R}{{{R_0}}}} \right) \to t$ versus $t$ and obtain the value of half-life from the graph.
The activity of a radioactive material is $2.56 \times 10^{-3} \,Ci$. If the half life of the material is $5$ days, after how many days the activity will become $2 \times 10^{-5} \,Ci$ ?
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- [JEE MAIN 2022]
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