Estimate the average kinetic energy of hydrogen atoms (or molecules) at room temperature and use the result to explain why nearly all H atom sare in the ground state at room temperature and hence emit no light.

Explanation

According to kinetic theory , the average KE of atoms or molecules in a gas is given by `bar"KE"=3/2kT`
where `k=1.38xx10^(-23)` J/K is Boltzmann's constant, and T is kelvin (absolute ) temperature. Room temperature is about T=300 K, so `bar"KE"=3/2(1.38xx10^(-23) J//K)(300K)=6.2xx10^(-21) J` , or , in electron volts :
`bar"KE"=(6.2xx10^(-21) J)/(1.6xx10^(-21) J//eV)=-0.04 eV`
The average KE of an atom as a whole is thus very small compared to the energy between the ground state and the next higher energy state (13.6 eV-3.4 eV=10.2 eV) . Any atoms in excited states quickly fall to the ground state and emit light. Once in the ground state, collisions with other atoms can transfer energy of only 0.04 eV on the average. A small fraction of atoms can have much more energy, but even a KE that is 10 times the average is not nearly enough to excite atoms above the ground state. Thus, a room temperature , nearly all atoms are in the ground state . Atoms can be excited to upper states by very high temperature, or by passing a current of high energy electrons through the gas, as in a discharge tube.