A radioactive nucleus undergoes a series of deacy according to the scheme.
`Aoverset(alpha)rarrA_(1)overset(beta^(-))rarrA_(2)overset(alpha)rarrA_(3)overset(gamma)rarrA_(4)`
If the mass number and atomic number of `A` are `180` and `172` respectively, what are these numbers for `A_(4)`.

Explanation

in`alpha -" Decay",""_(Z)^(A)Xto ""_(Z-2)^(A-4)Y+""_(2)^(4)He`
`here , ""_(72)A^(180) overset(alpha)to ""_(70)A_(1)^(176)+""_(2)^(4)He`
in `beta^(-) "decay" ,""_(Z)^(A)Xto ""_(Z+1)^(A)Y+e^(-)+barv`
` here, ""_(70)A_(1)^(176) overset(beta)to""_(71)A_(2)^(176)+e^(-)+barv`
`"again", ""_(71)A_(2)^(176)overset(alpha)to ""_(69)A_(3)^(172)+""_(2)^(4)He`
in `gamma`-decay, `""_(Z)^(A)Xto ""_(Z)^(A)X+gamma ""_(69)A_(3)^(172)+gamma`
so , we have ,
`""_(72)A^(180)overset(alpha)to ""_(70)A_(a)^(176)overset(beta)to""_(71)A_(2)^(176)overset(alpha)to ""_(69)A_(3)^(172)overset(gamma)to ""_(69)A_(4)^(172)`