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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 (original) mass `(N_(0))` = 1 hram
Reduced mass = 2 mg = 0.002 grams
Final mass (N) = 1-0.002 = 0.998 grams
t = 5 years
`e^(-lambda t)=(N)/(N_(0))rArr e^(lambda t)=(N_(0))/(N)rArr lambda t = log_(e )[(N_(0))/(N)]`
`lambda t = 2.303 log [(N_(0))/(N)]`
`lambda t = 2.303 log [(1)/(0.998)]`
`= 2.303 log (1.002)`
`= 2.303xx0.000868`
`= 0.001999`
`lambda = (0.001999)/(5)=0.0003998`
`T = (0.693)/(lambda)=(0.693)/(0.0003998)=1733.3` years
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