  A chiral quark-model approach is adopted to study the $\gamma p\rightarrow
\pi^0p$ and $\gamma n\rightarrow \pi^0 n$ reactions. Good descriptions of the
total and differential cross sections and single-polarization observables are
obtained from the pion production threshold up to the second resonance region.
It is found that (i) the $n=0$ shell resonance $\Delta(1232)P_{33}$, the $n=1$
shell resonances $N(1535)S_{11}$ and $N(1520)D_{13}$, and the $n=2$ shell
resonance $N(1720)P_{13}$ play crucial roles in these two processes. They are
responsible for the first, second and third bump structures in the cross
sections, respectively. (ii) Furthermore, obvious evidences of $N(1650)S_{11}$
and $\Delta(1620)S_{31}$ are also found in the reactions. They notably affect
the cross sections and the polarization observables from the second resonance
region to the third resonance region. (iii) The $u$-channel background plays a
crucial role in the reactions. It has strong interferences with the $s$-channel
resonances. (iv) The $t$-channel background seems to be needed in the
reactions. Including the $t$-channel vector-meson exchange contribution, the
descriptions in the energy region $E_\gamma= 600\sim 900$ MeV are improved
significantly. The helicity amplitudes of the main resonances,
$\Delta(1232)P_{33}$, $N(1535)S_{11}$, $N(1520)D_{13}$, $N(1720)P_{13}$,
$N(1650)S_{11}$ and $\Delta(1620)S_{31}$, are extracted and compared with the
results from other groups.
