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How much .84Po^210 of half-life 138 days...

How much `._84Po^210` of half-life 138 days is required to produce a source of `alpha`-radiation of intensity 5 mCl (millicurie ) ?

Text Solution

Verified by Experts

Decay constant, `lambda=0.693/T=0.693/(138xx24xx60xx60)s^(-1)`
Activity, A=5 mCl `=5xx3.70xx10^7` dps
Now, `A=lambdaN`
or, `N=A/lambda=(5xx3.7xx10^7xx138xx24xx60xx60)/0.693`
Again, number of atoms contained in 210 g `P^210`
=Avogadro's number =`6.023xx10^23`
Hence, mass of N such particles
`=(210xx5xx3.7xx10^7)/(6.023xx10^23)xx(138xx24xx60xx60)/0.693`
`=1.11xx10^(-6)` g (approx. )
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