Question
A radioactive nucleus ${ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X}$ 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
Initially element is represented by ${ }_z x^A$
$\beta$ particle is represented by $-1 e^{\circ}$ after emitting a $\beta$ particle atomic number of element would increase by 1 unit and mass number of element would remain unchanged.
So after emitting a $\beta$ particle ${ }_z x^A$ would become ${ }_{z+1} x^A$
a particle is rep resented by ${ }_2 He ^4$ 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 $_{z+1-2}X^{A-4} = _{z-1}X^{A-4}.$
The daughter nucleus is represented by $_QY^P.$
$_Qy^P =_{z-1}X^{A-4.}$
$P= A-4.$
$Q= Z-1.$
$\beta$ particle is represented by $-1 e^{\circ}$ after emitting a $\beta$ particle atomic number of element would increase by 1 unit and mass number of element would remain unchanged.
So after emitting a $\beta$ particle ${ }_z x^A$ would become ${ }_{z+1} x^A$
a particle is rep resented by ${ }_2 He ^4$ 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 $_{z+1-2}X^{A-4} = _{z-1}X^{A-4}.$
The daughter nucleus is represented by $_QY^P.$
$_Qy^P =_{z-1}X^{A-4.}$
$P= A-4.$
$Q= Z-1.$
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