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/t_1/2 = 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