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13.Nuclei
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એક રેડિયો એક્ટિવ નમૂનાનો $10\%$ ક્ષય થવા લાગતા ......... વર્ષ શોધો જેનું અર્ધ આયુષ્ય $22$ વર્ષ છે.
A
$22$
B
$10$
C
$57$
D
$73$
Solution
$\frac{N}{{{N_0}}}\,\, = \,\,\,{\left( {\frac{1}{2}} \right)^{t/T}}\,\,\,\,\,\, $
$\Rightarrow \,\,\,\,{\left( {\frac{1}{2}} \right)^{t/22}} = \,\,\frac{{10}}{{100}}$
અથવા $\,10\,\, = \,\,\,{2^{t\,/22}}$ અથવા ${\log _{10}}10\,\, = \,\,\frac{t}{{22}}\,\,{\log _{10}}2$
$t\,\, = \,\,\frac{{22{{\log }_{10}}10}}{{{{\log }_{10}}2}}\,\, = \,\,\frac{{22\,\, \times \,\,1}}{{0.3010}}\,\, \approx \,\,73\,\,years$
Standard 12
Physics
