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1 g of .(79)Au^(198) (t(1//2) = 65 hr) d...

`1 g` of `._(79)Au^(198) (t_(1//2) = 65 hr)` decays by `beta`-emission to produce stable `Hg`.
a. Write nuclear reaction for process.
b. How much `Hg` will be present after 260 hr.

Text Solution

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a. `._(79)Au^(198) rarr ._(80)Hg^(198) ._(-1)e^(0)`
b. `t_(1//2) = 65 hr`
`T = 260 hr`
`:' T = t_(1//2) xx n`
`:.` Number of halves `(n) = (260)/(65) = 4`
Now, amount left undcayed `(N) = (N_(0))/(2^(4)) = (1)/(2^(4)) = (1)/(16) g`
`:.` Amount of `Au` decayed `= (15)/(16) g`
`:' g Au` gives `198 g Hg`.
`:. (15)/(16) Au` gives `(15)/(6) Hg`.
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