A recent measurement of $^{4}\mathrm{He}$ photodisintegration reactions, $^{4}\mathrm{He}(\ensuremath{\gamma},p)^{3}\mathrm{H}$ and $^{4}\mathrm{He}(\ensuremath{\gamma},n)^{3}\mathrm{He}$ with laser-Compton photons shows smaller cross sections than those estimated by other previous experiments at ${E}_{\ensuremath{\gamma}}\ensuremath{\lesssim}30\text{ }\text{ }\mathrm{MeV}$. We study big bang nucleosynthesis with the radiative particle decay using the new photodisintegration cross sections of $^{4}\mathrm{He}$ as well as previous data. The sensitivity of the yields of all light elements D, T, $^{3}\mathrm{He}$, $^{4}\mathrm{He}$, $^{6}\mathrm{Li}$, $^{7}\mathrm{Li}$, and $^{7}\mathrm{Be}$ to the cross sections is investigated. The change of the cross sections has an influence on the nonthermal yields of D, $^{3}\mathrm{He}$, and $^{4}\mathrm{He}$. On the other hand, the nonthermal $^{6}\mathrm{Li}$ production is not sensitive to the change of the cross sections at this low energy, since the nonthermal secondary synthesis of $^{6}\mathrm{Li}$ needs energetic photons of ${E}_{\ensuremath{\gamma}}\ensuremath{\gtrsim}50\text{ }\text{ }\mathrm{MeV}$. The nonthermal nucleosynthesis triggered by the radiative particle decay is one of candidates of the production mechanism of $^{6}\mathrm{Li}$ observed in metal-poor halo stars. In the parameter region of the radiative particle lifetime and the emitted photon energy, which satisfies the $^{6}\mathrm{Li}$ production above the abundance level observed in metal-poor halo stars, the change of the photodisintegration cross sections at ${E}_{\ensuremath{\gamma}}\ensuremath{\lesssim}30\text{ }\text{ }\mathrm{MeV}$ as measured in the recent experiment leads to $\ensuremath{\sim}10%$ reduction of resulting $^{3}\mathrm{He}$ abundance, whereas the $^{6}\mathrm{Li}$ abundance does not change for this change of the cross sections of $^{4}\mathrm{He}(\ensuremath{\gamma},p)^{3}\mathrm{H}$ and $^{4}\mathrm{He}(\ensuremath{\gamma},n)^{3}\mathrm{He}$. The $^{6}\mathrm{Li}$ abundance, however, could show a sizable change and therefore the future precise measurement of the cross sections at high energy ${E}_{\ensuremath{\gamma}}\ensuremath{\gtrsim}50\text{ }\text{ }\mathrm{MeV}$ is highly required.