Q (a) Draw the energy level diagram showing the emission of beta particles followed by gamma rays by a Co ( Z=27 A=60 ) nucleus.

(b) Plot the distribution of kinetic energy of beta particles and state why the energy spectrum is continuous.

Part (b) is my doubt.

Dear Student
For the 1st part  refer to NCERT page 451 section 13.6.4
Now for the plot of KE of B particle refer the graph given below :


Now coming to the point why the spectrum is continious it is because beta particles share their energy with an antineutrino or neutrino, the beta energy spectrum is continuous. The energy of the beta particle varies continuously between zero and a maximum value, which is specific to the beta emitting radionuclide. At the maximum particle energy, the antineutrino or neutrino, has zero kinetic energy. 
Thank you!  :)
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