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

How many `alpha` and `beta`-particles are emitted when U-238 changes to Pb-206 due to radioactivity. Atomic numbers of U-238 and Pb-206 are 92 and 82 respectively.

Text Solution

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As per displacement rule, loss of mass number due to emission of an `alpha`-particle is 4 and that due to emission of `beta`- particle is nil. Also decrease in atomic number due to `alpha`-emission is 2 and increase in atomic number due to `beta`-emission is +1.
Let x and y be the required number of `alpha` and `beta`-emission for the transmutation .
`therefore` 4x+0 = 238-206 =32
or , `x=32/4=8`
Again, the reduction in atomic number due to `alpha` -emission =2x
and increase in atomic number due to `beta`-emission =y.
`therefore` Total reduction in atomic number =2x-y
Now , according to the question ,
2x-y=92-82=10
or, y=16-10=6
Hence, 8 `alpha` - particles and 6 `beta`-particles are emitted.
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