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192. Problem 3.34 (R) The nucleus of a carbon atom initially at rest in the laboratory goes from one state to another by emitting a photon of energy 4.43 MeV. The atom in its final state has a rest mass of 12.0000 amu. (1 amu corresponds to 931.478 MeV). We have to find (a) the momentum of the carbon atom after the decay, as measured in the laboratory; (b) the kinetic energy, in MeV, of the carbon atom after the decay, as measured in the laboratory system. |
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Solution: Click For PDF Version (a) Energy of the photon emitted by the carbon atom,
Momentum of the photon,
As the carbon atom was at rest when it emitted the photon, and as the
momentum is conserved, the magnitude of the momentum of the atom after it has
emitted the photon will be equal to that of the photon. Therefore, the momentum
of the carbon atom as measured in the laboratory frame will be
(b) Mass of the carbon atom after it has emitted the photon,
Kinetic energy of the carbon atom after it has emitted the photon will be
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