  It is widely believed that Hawking radiation originates from excitations near
the horizons of black holes. However, Giddings proposed that the Hawking
radiation spectrum that characterizes evaporating semi-classical black holes
originates from a quantum atmosphere, which extends beyond the horizon of a
black hole. Although several research projects have been conducted in this
field, they have not yet taken into account the effect of R\'enyi entropy. In
the present article, we will therefore consider the effect of R\'enyi entropy
on Hawking radiation power. We assume that if the effect of R\'enyi entropy is
very small, we suggest that the Hawking radiation should originate from the
quantum atmosphere which extends beyond the black hole's horizon for finite
dimensions. That is, that Giddings' suggestion is the more likely of the above
possibilities. However, for infinite dimensions, both suggestions are equally
credible. We briefly consider the very large effect of R\'enyi entropy on
Hawking radiation power as well. We find that if the effect of R\'enyi entropy
is very large and {\omega}/T_{BH} is very small, then the power spectral
density S_R is proportional to the power spectral density S_{BH}.
