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How many alpha and beta - particles are...

How many `alpha and beta ` - particles are emitted when uranium nucleus `(""_(92)^(238)U)` decay to `""_(82)^(214)Pb` ?

Text Solution

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Let n be the number of `alpha` - particles and m be the number of `beta` - particles emitted.
`""_(92)U^(238)rarr ""_(82)Pb^(214)+n_(2)He^(4)+m""_(-1)e^(0).`
As mass is conserved , 238 = 214 + 4n + m (0)
`= 214 + 4n implies 4n = 24 , n = 6`
As charge is conserved , 92 = 82 + 2n + m (-1)
10 = 2 (6) - m `( :. n = 6) implies m = 2 `
`:. 6 alpha` particles and `2 beta` - particles are emitted
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