I'm trying to solve this problem:
A silicon photo-diode has a responsivity of 0.6 A/W at a wavelength of 850 nm. Determine the minimum incident optical power at the photo-diode at this wavelength in order to maintain a bit rate of \$10^{-7},\$ when utilizing NRZ signaling at a rate of 35 Mbit/s.
and I solved it by:
\begin{align*} R=&{0.6}{A/W}&\\ \lambda =& {850}{nm}={0.850}{\mu m}&\\ B =&{10^{-7}}{b/s}&\\ \textrm{BER}=& \exp(N_p)/2&\\ N_p=&\ln (2\times \textrm{BER})&\\ =&\ln (2\times ({10^{-7}}{b/s}))&\\ =& -15.425&\\ P_{\textrm{rec}}=& N_p \hbar \nu B/2 &\\ =& (-15.425)(6.6\times 10^{-34}) \Big(\dfrac{3\times 10^8}{ {850}{nm}}\Big)({35}{Mbit/sec}/2) \end{align*}
However, I've seen answers assuming that \$E=N\hbar \nu /\eta\$, \$E=P_i 2/B\$, and \$BER=e^{-N_p}\$. Any idea why they assumed that?