1. The problem statement, all variables and given/known data A container holds N molecules of nitrogen gas at T = 280K. Find the number of molecules with kinetic energies between .0300 eV and .0312 eV. dE = .0012 eV E = .0306 eV kT = 3.8668*10^-21 J or .02413 eV 2. Relevant equations N(E) = (2N)(E^1/2)(e^(-E/kT)(π^-1/2)((kT)^-3/2) (defines the energy distribution of the gas) dN = N(E)dE dN = (2N)(E^1/2)(e^(-E/kT)(π^-1/2)((kT)^-3/2)dE 3. The attempt at a solution I assumed that N(E) can be approximated to be linear therefore the above equation can be used. E was found to be the average energy between the two given values and dE was found by taking the difference between the two given energy values. kT was found by multiplying Boltzmann's constant (1.381*10^-23) and multiplying by the given temperature. The answer is supposed to be in terms of N (the overall number of molecules in the volume). I calculated the number to be (2)(N)(.175 ev^1/2)(.281)(.5642)(266.79 ev^3/2)(.0012 eV) = .0178 N However, the actual answer turns out to be 6.1 * 10^-6 N. I can't figure out what I've done incorrectly and any help would be appreciated!