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A uranium nucleus .(92)U^(238) emits and...

A uranium nucleus `._(92)U^(238)` emits and `alpha`-particle and a `beta`-particle in succession. The atomic number and mass number of the final nucleus will be

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`F=(1)/(4pi epsilon_(0))(q_(1)q_(2))/(R^(2))`
`""_(92)U^(238)` has charge 92e. When `alpha`-particle is emifted, charge on residual nucleus is `92e-2e=90e`
`:." "q_(1)=90e,q_(2)=2e`, and `R=9xx10^(-75)` m
`:." "F=9xx10^(9)xx((90e)(2e))/((9xx10^(-15))^(2))`
`=(9xx10^(9)xx90xx(1.6xx10^(-19))^(2)xx2)/((9xx10^(-15))^(2))=512` N
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