A radioactive nucleus $A$ with a half life $T$, decays into a nucleus $B.$ At $t = 0$, there is no nucleus $B$. At sometime $t$, the ratio of the number of $B$ to that of $A$ is $0.3$. Then, $t$ is given by
A radioactive nucleus $A$ with a half life $T$, decays into a nucleus $B.$ At $t = 0$, there is no nucleus $B$. At sometime $t$, the ratio of the number of $B$ to that of $A$ is $0.3$. Then, $t$ is given by
- [JEE MAIN 2017]
- A
$t = \frac{T}{2}\;\frac{{\log 2}}{{\log 1.3}}$
- B
$t = T\;\frac{{\log 1.3}}{{\log 2}}$
- C
$t=T \log(1.3)$
- D
$t = \frac{T}{{{{log}}\left( {1.3} \right)}}$
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- [JEE MAIN 2023]