How many alpha and `beta^(-)` decays does `U^(238)` experiences before turning finally into stable `Pb^(206)` isotope ?

Explanation

Let n be the number of `alpha`-particles and m be the number of `beta`-particles emitted .
`._92U^238 to ._82Pb^214 + n_2He^4 + m ._(-1)e^0`.
As mass is conserved , 238=214+4n+m(0)
=214+4n
4n=24 , n=6
As charge is conserved , 92=82+2n+m(-1)
10=2(6)- m (`because` n=6) , m=2
`therefore 6 alpha`- particles and `2 beta`- particles are emitted.