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Obtain the maximum kinetic energy of bet...

Obtain the maximum kinetic energy of `beta`-particles, and the radiation frequencies of `gamma` decays in the decay scheme shown in Fig. `14.6`. You are given that `m(.^(198)Au)=197.968233 u, m(.^(198)Hg)=197.966760 u`

Text Solution

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Energy corresponding to `gamma_1`
`E_1=1.088-0=1.088MeV`
`1.088xx1.6xx10^(-13)"joule"`
`:.` Frequency, `v(gamma_1)=(E_1)/h=(1.088xx1.6xx10^(-13))/(6.6xx10^(-34))`
`=2.63xx10^(20)Hz`
Similarly, `v(gamma_2)=(E_2)/h=(0.412xx1.6xx10^(-13))/(6.6xx10^(-34)) =9.98xx10^(19)Hz`
and `v(gamma_3)=(E_3)/h=((1.088-0.412)xx1.6xx10^(-13))/(6.6xx10^(-34)) =1.64xx10^(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)]xx931MeV`
`=[m(._(79)Au^(198))-m(._(80)Hg^(198))-1.088/931]xx931MeV`
`=931[197.968233-197.966760]-1.088MeV=1.371-1.088`
`=0.283MeV`
Similarly, `K_(max)(beta_2)=0.957MeV`
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