${}^{22}\mathrm{Ne}$ nucleus, after absorbing energy, decays into two $\alpha$-particles and an unknown nucleus. The unknown nucleus is

Atomic number of neon is $10$.

By the emission of two $\alpha$ - particles, atomic number will be reduced by $4$.

Therefore, atomic number of the unknown element will be $Z=10-4=6$.

Similarly, mass number of the unknown element will be
$A=22-$($2\times 4$)$=14$
Therefore, unknown nucleus is carbon $(A=14, Z=6)$