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One gram of radium is reduced by 2 milli...

One gram of radium is reduced by 2 milligram in 5 years by `alpha`- decay. Calculate the half-life of radium.

Text Solution

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Initial mass `= 1 g, t = 5` years
Reduced mass `= 2mg = 2x 10^(-3) g = (2)/(1000)g`
Remaining mass `=1 - (2)/(1000) = (998)/(1000) g`
`(N)/(N _(0)) = (998)/( 1000) (because` Mass `prop` Number of atoms)
`(N)/(N _(0)) = e ^(- lamdat) = e ^(5 lamda) implies log _(e) ((1000)/(998)) = 5 lamda`
`2.303 (3.000-2.9991) = 5 lamda`
`lamda = (2. 303 xx 1 xx 0.0009)/(5 )`
`(T _(1//2)) = (0.693)/(lamda ) = ( 0.693xx 5 )/(2.303 xx 0.0009) = 1671. 7` years
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