If the de-Broglie wavelength of a proton is $100 \mathrm{fm}$, $\left(\mathrm{a}\right)$ What is the speed of the proton and $\left(\mathrm{b}\right)$ through what electric potential would the proton have to be accelerated to acquire this speed?

A light detector has an absorbing area of $3.00\times {10}^{-6}{\mathrm{m}}^2$ and absorbs $50\%$ of the incident light, which is at wavelength $600 \mathrm{nm}.$ The detector faces an isotropic source, $12.0 \mathrm{m}$ from the source. The energy $E$, emitted by the source, versus time $t$ is given in the figure.$(E_{\mathrm{s}}=7.2 \mathrm{nJ}, t_{\mathrm{s}}=2.0 \mathrm{s})$ At what rate are the photons absorbed by the detector?