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Obtain the maximum kinetic energy of β-particles, and the radiation frequencies of γ decays in the decay scheme shown in Fig. 13.6. You are given that

m (198Au) = 197.968233 u

m (198Hg) =197.966760 u

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It can be observed from the given γ-decay diagram that γ1 decays from the 1.088 MeV energy level to the 0 MeV energy level. Hence, the energy corresponding to γ1-decay is given as: E1 = 1.088 − 0 = 1.088 MeV hν1= 1.088 × 1.6 × 10−19 × 106 J Where, h...
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It can be observed from the given γ-decay diagram that γ1 decays from the 1.088 MeV energy level to the 0 MeV energy level.

Hence, the energy corresponding to γ1-decay is given as:

E1 = 1.088 − 0 = 1.088 MeV

hν1= 1.088 × 1.6 × 10−19 × 106 J

Where,

h = Planck’s constant = 6.6 × 10−34 Js

ν1 = Frequency of radiation radiated by γ1-decay

It can be observed from the given γ-decay diagram that γ2 decays from the 0.412 MeV energy level to the 0 MeV energy level.

Hence, the energy corresponding to γ2-decay is given as:

E2 = 0.412 − 0 = 0.412 MeV

hν2= 0.412 × 1.6 × 10−19 × 106 J

Where,

ν2 = Frequency of radiation radiated by γ2-decay

It can be observed from the given γ-decay diagram that γ3 decays from the 1.088 MeV energy level to the 0.412 MeV energy level.

Hence, the energy corresponding to γ3-decay is given as:

E3 = 1.088 − 0.412 = 0.676 MeV

hν3= 0.676 × 10−19 × 106 J

Where,

ν3 = Frequency of radiation radiated by γ3-decay

Mass of = 197.968233 u

Mass of = 197.966760 u

1 u = 931.5 MeV/c2

Energy of the highest level is given as:

β1 decays from the 1.3720995 MeV level to the 1.088 MeV level

∴Maximum kinetic energy of the β1 particle = 1.3720995 − 1.088

= 0.2840995 MeV

β2 decays from the 1.3720995 MeV level to the 0.412 MeV level

∴Maximum kinetic energy of the β2 particle = 1.3720995 − 0.412

= 0.9600995 MeV

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