Parent element is 22688Ra
Atomic mass =226
Atomic number =88
RaC is formed after the emission of 3 alpha particles. Mass of 3 alpha particles =3×4=12
So, atomic mass of RaC=(226−12)=214
With emission of one α-particle, atomic number is decreasd by 2 and with the emission of one β-particle, atomic number is increased by 1.
So, Atomic number of RaC=88−(3×2)+1=83