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How many alpha and beta-particles are em...

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

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) to "" _(52) Pb ^(214) + n ("" _(2)He^(4)) + m ("" _(-1)e ^(0)).`
As mass is conserved, `= 238=214 + 4n + m(0)`
`= 214 + 4n, 4n = 24, n =6`
As change is conserved, `92 = 82+ 2n +m (-1)`
` 10=2 (6) - m (because n =6) , m =2.`
`therefore 6 alpha-` particles and `2 beta-` particles are emitted
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