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J Ravi Kiran Grade: 11
        

A scientist wanted to perform an experiment requiring beta particles at the rate of atleast 400 beta particles/minute.  He ordered 10-16g-atoms sample of 53I131, beta emitter with half life 8 days.  During transportation of pure53I131 16 day were lost.  How long would the scientist be able to do above experiment.

7 years ago

Answers : (1)

Ramesh V
70 Points
										

The source is useful until it emits at the rate of 400 beta particles/min or more.


1 mole of  I-131 isotope = 131 g


no. of Iodine nuclie in 131 g of  I-131 = 6.023 x 1023 atoms


Thus no. of radioactive atoms in 10-16 g of I-131 = 6.023 x 1023  x 10-16 / 131 = 459770 atoms


If half life = 8 days  = 11520 min


Thus lambda = 0.693/t1/2 = 0.693/11520 = 6.015 x 10-5 min-1


Now atoms remaining after 16 days or 2 half lives = 459770/4 = 114943 atoms


Thus activity after 16 days i.e beta particles emitted per minute = 114943 x exp (-lambda )


= 11493 exp(-6.015 x 10-5 )


now the time for which source can be used is until


11493 exp(-6.015 x 10-5 *t)  > 400


Now solve for t = 55575.5 days


152 years 95.5 days


--


regards


Ramesh

7 years ago
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