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  • Assuming  of trace radioactive element <img alt="\mathrm{X}" src="https://entra

Assuming 1 \mu \mathrm{g} of trace radioactive element \mathrm{X} with a half life of 30 years is absorbed by a growing tree. The amount of \mathrm{X} remaining in the tree after 100 years is _______\mathrm{\times 10^{-1} \mathrm{\mu g}}.

\mathrm{\text { [Given: } \ln 10=2.303 ; \log 2=0.30]}

Option: 1

1


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{t_{1 / 2}=30 \text { years } k=\frac{\ln 2}{30 \text { years }}}
\mathrm{A_{0}=14 \mathrm{~g}\quad\; \; t=100 \text { year } }

\mathrm{\frac{2.303 \log 2}{30}=\frac{2.303}{100}\quad \frac{1 \mu \mathrm{g}}{A_{t}} }
\mathrm{\frac{10}{3}\log 2= \log \frac{1}{A_{t}}\quad \quad 0.01=\log \frac{1}{A_{t}} }

\mathrm{A_{t}= 0.1 \, \mu g= 1\times 10^{-1}\mu g }

Hence answer is 1.
 

Posted by

Pankaj

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