When the nucleus of 238 U 92 disintegrates to give one nucleus of U 82 206 ; the number of α -particles emitted and the number of β -particles emitted is

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When an α particle is emitted, the atomic number decreases by 2 and the mass number decreases by 4.

The number of alpha particles emitted is

$N_{α} = \frac{238 - 206}{4} = \frac{32}{4} = 8$ .

When 8 alpha particles are emitted the atomic number decreases by 2×8=16, from 92 to 92−16=76. When a β particle is emitted, the atomic number increases by 1. The number of β particles emitted is

$N_{β} = 82 - 76 = 6$

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