  In-situ ${\gamma}$-ray measurements were performed using a portable high
purity germanium spectrometer in Hall-C at the second phase of the China
Jinping Underground Laboratory (CJPL-II) to characterise the environmental
radioactivity background below 3 MeV and provide ambient ${\gamma}$-ray
background parameters for next generation of China Dark Matter Experiment
(CDEX). The integral count rate of the spectrum was 46.8 cps in the energy
range of 60 to 2700 keV. Detection efficiencies of the spectrometer
corresponding to concrete walls and surrounding air were obtained from
numerical calculation and Monte Carlo simulation, respectively. The
radioactivity concentrations of the walls in the Hall-C were calculated to be
${6.8\pm1.5}$ Bq/kg for ${^{238}}$U, ${5.4\pm0.6}$ Bq/kg for ${^{232}}$Th,
${81.9\pm14.4}$ Bq/kg for ${^{40}}$K. Based on the measurement results, the
expected background rates from these primordial radionuclides of future CDEX
experiment were simulated in unit of counts per keV per ton per year (cpkty)
for the energy ranges of 2 to 4 keV and around 2 MeV. The total background
level from primordial radionuclides with decay products in secular equilibrium
are ${7.0 \times 10^{-2}}$ and ${3.1 \times 10^{-3}}$ cpkty for energy ranges
of 2 keV to 4 keV and around 2 MeV, respectively.
