1. The problem statement, all variables and given/known data The Ground state wave function governing the motion of a pair of vibrating nuclei looks like: wave function = wave (x) = (a/pi)1/4 e-ax2/2 where a = alpha = mu*w/(h bar), which is determined by mu = reduced mass of the pair where w = angular vibrational frequency ...So, suppose the vibrating atoms in question were C and O. Compute what v~, the frequency of the vibration in cm-1, would have to be if the root-mean square fluctation in bond length were 0.035Angstom. I lost track of the units for my solution, and I am not sure if I have done correctly... 2. Relevant equations wave function = wave (x) = (a/pi)1/4 e-ax2/2 a = alpha = mu*w/(h bar), which is determined by mu = reduced mass of the pair w = angular vibrational frequency root mean square = <x2> - <x>2 3. The attempt at a solution root mean square = <x2> - <x>2 where <x2> = integral (-infinite to infinite) wave(x) x2 wave(x) dx = which I got 1/(2a) as a result <x> = integral (x=o to L) p(x) x p(x) dx which I got as 0 in the end so...I input: root mean square = <x2> - <x>2 = 1/(2a) - 0 = 1/(2a) since root mean square = 0.035 angstrom = 1/(2a) and b/c a = mu*w/(h bar), I rearranged so that: w = (h bar)/(0.07mu)...where mu = m1m2/(m1 + m2) For mass of 1 C atom: 12.01g/(6.022x1023 atoms) x 1kg/103g = 1.99 x 10-26kg For mass of 1 O atom: 16.00g/(6.022x1023 atoms) x 1kg/103g = 2.66 x 10-26kg mu = 1.14 x 10-20kg therefore w = (h/(2pi))1/(0.07mu) = 1.32 x 10-13 omega (is this right????) I know h has units of J*2 and mu = kg.....but together they do NOT make omega..... therefore v~ = w/(2pi*c) where c = speed of light = 1.32 x 10-13 (assuming the unit is correct) / (2pi*3x108m/s) = 7.02 x 10-23 s-1 b/c I got lost track of units....I am not sure if the units in the solution is right...if someone could (1) explain the units in each calculations I did and then (2) give me hints as how to keep track of units for near future too, that would be so wonderful.