  Using an \emph{empirical} description of a prompt GRB pulse, we analyze the
individual pulses of all Fermi/GBM GRBs with known redshifts, till July 2009.
This description is simultaneous in time and energy and allows one to determine
the peak energy of Band spectrum at zero fluence ($E_{peak,0}$). We
demonstrate, for the first time, that the $E_{peak,0}$ bears a very strong
correlation with the isotropic energy of the individual pulses, and hence, each
pulse can be used as a luminosity indicator. As a physical description is
needed in order to use GRB pulses for cosmological purposes, we explore other
physical spectral models. As pulses are the building blocks of a GRB, we choose
another sample of Fermi/GBM GRBs having bright, long and single/ separable
pulse(s) and fit the time-resolved spectra of the individual pulses with the
Band model and a model consisting of a blackbody and a power-law. Both these
models give acceptable fits. We find that the peak energy/ temperature always
decreases exponentially with fluence in the later part of a pulse. We
investigate multiple spectral components in the initial rising part and provide
a comprehensive empirical description of the spectral and timing behaviour of
prompt GRB pulses. This work strongly extends the possibility of using GRB
pulses as standard candles and the spectral parameters as proxy for redshift.
