Suppose a hydrogen atom is a distance $d$ away from a star (approximate the star as a blackbody). The radius of the star is $R$ and the its temperature is $T$. The hydrogen atom absorbs photons from the star and goes from $1s$ to $2p$ state. It gains the photon's momentum, but in a short time $\Delta t$, the atom emits the photon isotropically, meaning the momentum change due to the emission of photons is $0$. I am now looking for the force due to the absorption of the photons.
We can use Stefan-Boltzmann's law to find the energy flux that goes through the hydrogen atom at that tiny sold angle. We can also find the force through the following equation,\begin{equation} F = \frac{I}{\Delta t} = \frac{\Delta p}{\Delta t}\end{equation}where $I$ is the impulse and the $\Delta p$ is the change of momentum. It seems difficult to relate the energy flux to the change of momentum because only one specific frequency can excite the $1s$ state to $2p$. I am also unsure if we need to refer to the Einstein coefficient to find the transition rate.
