How may `alpha-` and `beta-` particles will be emitted when `._(90)Th^(232)` changes into `._(82)Pb^(208)`?

Explanation

`._(90)Th^(232) rarr ._(82)Pb^(208) + x ._(2)He^(4) + y ._(-1)e^(0)`
Remembering that the total atomic number as well as mass number must be equal to the two sides of the equation, we have
`208 + 4x + 0y = 232`
i.e., `4x = 24`
and `82 + 2x - y = 90`
or `2x - y = 8`
Solving Eqs. (i) and (ii), we get `x = 6` and `y = 4`.