In a $p-i-n$ photodiode, a pulse of light containing $8 \times 10^{12}$ incident photons at wavelength $\lambda_0=1.55~ \mu \mathrm{m}$ gives rise to an average $4 \times 10^{12}$ electrons collected at the terminals of the device. The quantum efficiency of the photodiode at this wavelength is___________$\%$.
- $50$
- $54.2$
- $62.5$
- $80$