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Q.
A radioactive atom $^{X}_{Y}M$ emits two $α$ particles and one $β$ particle successively. The number of neutrons in the nucleus of the product will be
An a-emission reduces the atomic mass by $4$ and atomic number by $2$, whereas a $\beta$-emission increases the atomic number by $1$ with no change in atomic mass
$M^{X}_{Y} \ce{->[-\alpha]}N^{X-4}_{Y-2} \ce{->[-\alpha]} O^{X-8}_{Y- 4} \ce{->[-\beta]}P_{Y-3}^{X-8}$
Number of neutrons = mass number - atomic number
$= X - 8 - Y + 3$
$ = X -Y -5$