An atom with an electron in a very high n state is said to be in aâRydberg state.â In Chap. 3 we learned that the radius of anelectron in state n is rn = n^ x h^2/4p^2 x me^2 = n^2 x r(B) wherethe Bohr radius r(B) = 0.0525nm. The (classical) cross section inthis model is s = prn^2, and for large n this gets so large that itmakes no sense to think about a bound electron. Letâs do a veryrough calculation to see where this model breaks down.
⢠Assume you have a gas cloud with T = 104K and density n(H) = 1atom/cm^3. (Watch out: in this problem we have the energy level nand the density nH .) What is the rms speed of an H atom in thisgas, in cm/s?
⢠Assuming each atom has the cross section given above, what is themean free path for collisions (the formula in terms of rB andn)?
⢠If all the atoms move at vrms what is the mean time betweencollisions, tc (in terms of rB and n)?
⢠For large n, the decay time, td, to go from state n to state n -1 is roughly n2 times 50 ns. For n = 100, nH = 1 and T = 104,calculate tc and td. Which is larger? Does it make sense to talkabout a bound state for n = 100?
⢠Nowtaken=1000andwritedowntc andtd (bothintermsofthen=100answerand numerically). Which is larger? Does it make sense to talk abouta bound state for n = 1000
⢠Those calculations were for the diffuse gas between the stars.Now assume we are in a stellar atmosphere, and nH = 1024 atoms/cm3.For what n does tc = td? Does this mean collisions or decays happenmore often? Given this, why is the gas not completely ionized?
