In a radioactive series, `._(92)U^(238)` charges to `._(82)Pb^(206)` through `n_(1)`(`alpha`-decay processes) and `n_(2)`(`beta-`deacy processes)

Options

A. `n _(1) = 8, n _(2) = 8`
B. `n _(1) = 6 , n _(2) = 6`
C. `n _(1) = 8 , n _(2) = 6`
D. `n _(1) = 6, n _(2) = 8`

Answer

C

Explanation

`""_(92) ^( 238) U to ""_( 82) ^( 206) Pb + n _(1) alpha + n _(2 ) beta`
From conservation of mass number:
`238 = 20 6 + 4n _(1)`
`32 = 4n _(1)`
`implies n _(1) = 8`
From conservation of charge:
`92 = 82 + 2n _(1) - n _(2)`
`92 = 82 + 2 (8) - n _(2)`
`implies n _(2) = 6`