`gamma_(1)` की ऊर्जा
`E(gamma_(1))=(1.088-0)=1.088" MeV"`
`=1.088xx1.6xx10^(-13)" J"`
`gamma_(2)` की ऊर्जा
`E(gamma_(2))=(0.412-0)=0.412" MeV"`
`=0.412xx1.6xx10^(-13)" J"`
`gamma_(3)` की ऊर्जा
`E(gamma_(3))=(1.088-0.412)=0.676" MeV"`
`=0.676xx1.6xx10^(-13)" J"`
अब सूत्र `E=hv` से,
`v=(E)/(h)` जहाँ, h = प्लांक नियतांक
`v(gamma_(1))=(E(gamma_(1)))/(h)=(1.088xx1.6xx10^(-13))/(6.62xx10^(-34))`
`=2.63xx10^(20)" Hz."`
`v(gamma_(2))=(E(gamma_(2)))/(h)=(0.412xx1.6xx10^(-13))/(6.62xx10^(-34))`
`=9.96xx10^(19)" Hz."`
`v(gamma_(3))=(E(gamma_(3)))/(h)=(0.676xx1.6xx10^(-13))/(6.62xx10^(-34))`
`=1.63xx10^(20)" Hz."`
`beta_(1)^(-)` - क्षय को निम्न प्रकार से व्यक्त किया जा सकता है -
`""_(79)^(198)"Au"=""_(80)^(198)"Hg"+e^(-)+E(beta_(1)^(-))+E(gamma_(1))`
अत: `beta_(1)^(-)` की महत्तम गतिज ऊर्जा
`E(beta_(1)^(-))=[m_(N)(""_(79)^(198)"Au")-m_(N)(""_(80)^(198)"Hg")-m_(e)]c^(2)-E(gamma_(1))`
`=m[(""_(79)^(198)"Au")-79m_(e)-m(""_(80)^(198)"Hg")+80m_(e)-m_(e)]c^(2)-E(gamma_(1))`
`=m[(""_(79)^(198)"Au")-m(""_(80)^(198)"Hg")]c^(2)-E(gamma_(1))`
`=(197.968233-197.966760)uxx c^(2)-1.088" MeV"`
`=0.001473xx931.5("MeV")/(c^(2))xx c^(2)-1.088" MeV"`
`=1.3720995-1.088=0.284" MeV."`
`beta_(2)^(-)` - क्षय को निम्न प्रकार से व्यक्त किया जा सकता है -
`""_(79)^(198)"Au"to""_(80)^(198)"Hg"+e^(-)+E(beta_(2)^(-))+E(gamma_(2))`
अत: `beta_(2)^(-)` की महत्तम गतिज ऊर्जा
`E(beta_(2)^(-))=[m_(N)(""_(79)^(198)"Au")-m_(N)(""_(80)^(198)"Hg")-m_(e)]c^(2)-E(gamma_(2))`
`=m[(""_(79)^(198)"Au")-79m_(e)-m(""_(80)^(198)"Hg")+80m_(e)-m_(e)]c^(2)-E(gamma_(2))`
`=m[(""_(79)^(198)"Au")-m(""_(80)^(198)"Hg")]c^(2)-E(gamma_(2))`
`=1.372" MeV"-0.412" MeV"`
`=0.96" MeV."`
