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13.Nuclei
hard
$6$ દિવસ પછી અવિભંજીત ભાગ $7/8$ હોય,તો $10$ દિવસ પછી અવિભંજીત ભાગ કેટલો થાય?
A
$77/80$
B
$71/80$
C
$31/32$
D
$15/16$
Solution
$N = {N_0}{\left( {\frac{1}{2}} \right)^{t/{T_{1/2}}}}$
$\Rightarrow$ $t = \frac{{{T_{1/2}}{{\log }_e}\left( {\frac{{{N_0}}}{N}} \right)}}{{{{\log }_e}(2)}}$
$\Rightarrow$ $t \propto {\log _e}\frac{{{N_0}}}{N}$
$\Rightarrow$ $\frac{{{t_1}}}{{{t_2}}} = \frac{{{{\left( {{{\log }_e}\frac{{{N_0}}}{N}} \right)}_1}}}{{{{\left( {{{\log }_e}\frac{{{N_0}}}{N}} \right)}_2}}}$ $\frac{6}{{10}} = \frac{{{{\log }_e}(8/1)}}{{{{\log }_e}({N_0}/N)}}$
$\Rightarrow$ ${\log _e}\frac{{{N_0}}}{N} = \frac{{10}}{6}{\log _e}(8) = {\log _e}32$
$\Rightarrow$ $\frac{{{N_0}}}{N} = 32$
અવિભંજીત ભાગ $ = 1 – \frac{1}{{32}} = \frac{{31}}{{32}}$.
Standard 12
Physics
