Question

A radioactive nucleus `""_"Z"^"A"` X first emits a beta particle and then an alpha particle to give the resulting nucleus `""_"Q"^"P"` Y  What will be the values of P and Q in terms of A and Z?

Answer 1

Initially element is represented by  _zX^A

β particle is represented by _-1e° after emitting a β particle atomic number of element would increase by 1 unit and mass number of element would remain unchanged.

So after emitting a β particle _zX^A would become _z+1X^A
a particle is rep resented by ₂He⁴ this means it contains 2 protons and 2 neutrons so mass of a particle is 4 unit. Thus after emitting a particle mass number of element would decrease by 4 unit and atomic number of element would decrease by 2.

So after emitting a particle _zX^A would become  _z+1-2X^A-4 = _z-1X^A-4.
The daughter nucleus is represented by _QY^P.
_Qy^P = _z-1X^A-4.
P= A-4.
Q= Z-1.