Question

Obtain the maximum kinetic energy of `beta`- particles, and the radiation frequencies of `gamma` decays in the decay scheme shown in Fig. You are given that
`m(.^(198)Au)=197.968233 u`
`m(.^(198)Hg)=197.966760 u`.

Answer 1

Energy corresponding to `r_(1)`
`E_(1)=1.088-0=1.088 MeV`
`= 1.088xx1.6xx10^(-13)` Joule
Frequency `v_(1)=(E_(1))/(h)`
`= (1.088xx1.6xx10^(-13))/(6.6xx10^(-34))`
`= 2.63xx10^(20)Hz`
similary `v_(2)=(E_(2))/(h)`
`= (0.412xx1.6xx10^(-12))/(6.6xx10^(10))`
`= 9.98xx10^(13)Hz`
and `v_(3)=(E_(3))/(h)`
`= ((1.088-0.412)xx1.6xx10^(-13))/(6.6xx10^(20)Hz)`
Maximum K.E. of `beta_(1)` particle
`K_("max")(beta_(1))=[m(._(79)Au^(198))-` mass of second excited state of `._(80)Hg^(198)]xx931 MeV`
`= [m(._(79)Au^(198))-m(._(82)Hg^(198))-(1.088)/(931)]xx931 MeV`
`= 931[197.968233-197.966760]-1.088 MeV`
`= 1.371-1.088=0.283 MeV`
similarly `k_("max")(beta_(2))=0.957 MeV`