Question

Bi with atomic no. 83 and mass no. 209 is produced from a parent element by the emission of 2alpha,4beta and one positron.what will be the parent element?

Answer 1

so let the parent nucleus be $X_{a}^b$
it undergoes 2α,4β emissions
in each alpha emission atomic mass decrease by 4 and atomic number decrease by 2
so after 2α emissions the nucleus will be $Y_{a-2(2)}^{b-2(4)}=Y_{a-4}^{b-8)}$
then 4β emissions so atomic number increases by 4(1 in each)
$Y_{a}^{b-8}$
then it also emits one positron so atomic number decreases by 1
$Y_{a-1}^{b-8}=Bi_{83}^{209}$
so b-8=209,b=217 a-1=83,a=84
so the parent nucleus is Polonium isotope $Po_{84}^{217}$

Answer 2

it is polonium Z=84 M=217