Posted by ANSST - SOLUTION
Problem Identifying:
“A nucleus, originally at rest, decays radioactively by
emitting an electron of momentum 1.73 MeV/c, and at right angles to the
direction of the election a neutrino with momentum 1.00 MeV/c. ( The MeV (million
electron volt) is a unit of energy, used in modem physics, equal to 1.60 x 10-8
erg. Correspondingly, MeV/c is a unit of linear momentum equal to 5.34 x 10-17
gm-cm/sec.) In what direction does the nucleus recoil? What is its momentum in
MeV/c? If the mass of the residual nucleus is 3.90 x 10-22 gm, what is its
kinetic energy, in electron volts? “
Solution:
Place the nucleus at the origin, and suppose the electron is
emitted in the positive y direction, and the neutrino in the positive x
direction. Then the resultant of the electron and neutrino momenta has
magnitude
and its direction males an angle
with the x axis. The nucleus must acquire a momentum of
equal magnitude and directed in the opposite direction. The kinetic energy of
the nucleus is
This is much smaller than the nucleus rest energy of several
hundred GeV, so the non-relativistic approximation is justified.