Using Boltzmann distribution law to find Temperature (1% of photons> 1eV)

[physicsofpeac]

Homework Statement

Use the Boltzmann distribution function to calculate the temperature at which 1.00% of a population of photons will have energy greater than 1.00 eV. The energy required to excite an atom is on the order of 1 eV.

The Attempt at a Solution

I attached my attempt but it only solves for temperature at which 1% of photons are at 2eV. I have no idea to find temperature at which 1% of photons are greater than 1eV.

 

[member 553083]

\begin{align}1.00\% &= \frac{N_{2eV}}{N}\\1.00\% &= \frac{e^{-2/kT}}{e^{-1/kT} + e^{-2/kT}}\\1.00\% &= e^{-2/kT}\\\log(0.01) &= -2/kT\\T &= -\frac{2}{k\log(0.01)}\end{align}