According to Rutherford Soddy law of radioactive decay, the rate of decay of radioactive along at any instant is proportional to the number of atoms present at that instant
dN
dt
=−λN Since λ = constant (decay constant) and N = number of atoms Rate of decay of Y particle is given as λxNx−λyNy=
dNy
dt
=0 [∵ Decay rate for β -particle become constant after some time] Given, rate of emission of β -particle =107/h ∴λxNx=λYNx=107/h