A nucleus with atomic number Z = 92 emits the following in a sequence: $\alpha ,{\beta }^{-},{\beta }^{-},\alpha ,\alpha ,\alpha ,\alpha ,\alpha {\beta }^{-},{\beta }^{-},\alpha ,{\beta }^{+},{\beta }^{+},\alpha$ . Then Z of the resulting nucleus is ___.

No. of $\alpha$ particles = 8

Atomic number decreases

By 8 x 2 = 16 units

$\alpha \to 2^{H{e}^4}$

No of ${\beta }^{-}$ particles  $(-1^{e^0})=4$

Atomic number increases by 4 units

$(+1^{e^0})$ no of ${\beta }^{+}$ particles released = 2

Atomic number decreases by 2

Resulting Atomic number

$\begin{array}{l}{Z}^1=Z-16+4-2\\ Z^1=92-14\\ Z^1=78\end{array}$