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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.
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
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regards
Ramesh
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