Hint: The maximum kinetic energy of β-particles is the maximum difference in the energy levels.
Step 1: Find the radiation frequencies of γ1-decay.
It can be observed from the given y-decay diagram that γ1-decay 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=1.088MeVhν1=1.088×1.6×10−19×106 Jwhere,h=Planck′s constant=6.6×10−34Jsν1=Frequency of radiation radiated by γ1−decay∴ν1=E1h=1.088×1.6×10−19×1066.6×10−34=2.637×1020 Hz
Step 2: Find the radiation frequencies of γ2-decay.
It can be observed from the given y-decay diagram that y2 decays from the 0.412 MeY energy level to the 0 MeV energy level.
Hence, the energy corresponding to y2-decay is given as:
E2=0.412−0=0.412MeVhν2=0.412×1.6×10−19×106 Jwhere,ν2=Frequency of radiation radiated by γ2−decay∴ν2=E2h=0.412×1.6×10−19×1066.6×10−34=9.988×1019 Hz
Step 3: Find the radiation frequencies of γ3-decay.
It can be observed from the given y-decay diagram that y3 decays from the 1.088 MeV energy level to the 0.412 MeV energy level.
Hence, the energy corresponding to y3-decay is given as:
E3=1.088−0.412=0.676MeVhν3=0.676×10−19×106Jwhere,v3= Frequency of radiation radiated by γ3−decay∴ν3=E3h=0.676×1.6×10−19×1066.6×10−34=1.639×1020Hz
Step 4: Find the maximum kinetic energy of β--particles.
Mass of m(A19878u)=197.968233 u
Mass of m(H19880g)=197.966760 u
1 u=931.5 MeV/c2
Energy of the highest level is given as:
E=[m(A19878u)-m(H19080g)]
=197.968233-197.966760=0.001473 u
=0.001473×931.5=1.3720995 MeV
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
