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The half life of ""(38) Sr^(90) isotope ...

The half life of `""_(38) Sr^(90)` isotope is 28 years. What is the rate of disintegration of 15 mg of this isotope? (Given Avogadro No `=6.023 xx 10^(23) )`

Text Solution

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`T_(1//2) = 28` years `= 28 xx 365 xx 24 xx 3600`
`T_(1//2) = 8.83 xx 10^(8)` seconds
`90g Sr_(38)^(90)` contains `6.0.23 xx 10^(23)` atoms
`N = (6.023 xx 10^(23) xx 15 xx 10^(-3))/(90) = 1.004 xx 10^(20)` atoms
`lambda = (0.693)/(T_(1//2)) = (0.693)/(8.83 xx 10^(8)) = 0.07848 xx 10^(-8)`
`lambda = 7.85 xx 10^(-10)`
Rate of disintegration
`R = lambda N`
`R = 7.85 xx 10^(-10) xx 1.004 xx 10^(20)`
`R = 7.8814 xx 10^(10)B q`
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