  We explore the energetics and plasma composition in FR II sources using a new
simple method of combining shock dynamics and radiation spectrum. The hot spots
are identified with the reverse shocked region of jets. With the
one-dimensional shock jump conditions taking account of the finite pressure of
hot ICM, we estimate the rest mass and energy densities of the sum of thermal
and non-thermal particles in hot spots. Independently, based on the Synchrotron
Self-Compton (SSC) model, we estimate the number and energy densities of {\it
non-thermal} electrons using the multi-frequency radiation spectrum of hot
spots. We impose the condition that the obtained rest mass, internal energy,
and number densities of non-thermal electrons should be lower than those of the
total particles determined by shock dynamics. We apply this method to Cygnus A.
We examine three extreme cases of pure electron-positron pair plasma (Case I),
pure electron-proton plasma with separate thermalization (Case II), and pure
electron-proton plasma in thermal-equilibrium (Case III). By detailed SSC
analysis for Cygnus A and 3C123, we find that the energy density of non-thermal
electrons is about 10 times larger than that of magnetic field. We find that
the Case III is not acceptable because predicted photon spectra do not give a
good fit to the observed one. We find that Case II can also be ruled out since
the number density of non-thermal electrons exceeds that of the total number
density. Hence, we find that only pure $e^{\pm}$ plasma (Case I) is acceptable
among the three cases. Total kinetic power of jet and electron acceleration
efficiency are also constrained by internal energy densities of non-thermal and
total particles.
