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Obtain the amount of .^60Co necessary to...

Obtain the amount of `.^60Co` necessary to provide a radioactive source of `8.0 Ci` strength. The half-life of `.^60Co` is `5.3` years?

Text Solution

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Half-life of `""_(27) ^(60) Co = 5.3` years
` =5.3 x 365 x 24 x 60 x 60`
`S = 5.3 x 3.15 x 10^(7) s`
Now .x. `gm of "" _(27) ^(60) Co` contains
` (10 ^(-3)x)/(60) k - ` mole ` = (x xx 10 ^(-3))/( 60 ) xx 6. 0 25 xx 10 ^(26)`
`N = 0.1004 4x x 10 ^(23) = 1.004 x xx 10 ^(22)` atoms
Required strength of `"" _(27) ^(60) Co = 8 m Ci`
`= 8 x 10 ^(-3) x 3.7 x 10 ^(10) dis//s`
We know that, decay rate `(R) = lamda N`
`N = (R)/(lamda) = ( 8xx 3.7 xx 10 ^(7))/( 0.693//T_(1//2))`
`= (29.6 xx 10 ^(7))/(0.693) x 5.3 x 1.5 x 10 ^(7)`
` = 713. 0909 x 10 ^(14)`
`1. 004 x x 10 ^(22) = 713. 0909 x 10 ^(14)`
`x = 710. 2499 x 10 ^(-8) kg = 7.1 x 10 ^(-6) g`
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