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13.Nuclei
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$99 \%$ of a radioactive element will decay between
A
$6$ and $7$ half lives
B
$7$ and $8$ half lives
C
$8$ and $9$ half lives
D
$9$ half lives
(AIIMS-2019)
Solution
The decay rate is given as,
$N=N_{0}\left(\frac{1}{2}\right)^{n}$
$\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{n}$
$\frac{1}{100}=\left(\frac{1}{2}\right)^{n}$
$2^{n}=100$
The number of half lives is calculated as,
$2^{n}=100$
$n$ lies between the $6$ and $7 .$ So, the radioactive element will decay between $6$ and $7$ half lives.
Standard 12
Physics
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