Question

the fundamental frequency of hcl

LICHOLULOI IL PILVIO U YUCULIOL Q3.) The fundamental vibrational frequency of HCl is 2889 cm 1. Suppose you introduce 100 molecules in a vessel and you want to predict the intensities in the IR spectra at 2000K. How many molecules will be in the first vibrational level, in the second and in the third?

Answer 1

To get the number of molecule in excited states, we must compare the two energies.

Thermal energy is a energy which gives energy to the molecule for excitation from lower energy level to next upper.

if spacing between energy level is greater than thermal energy kT them all molecule will remain in ground state.

Result-

here spacing between energy delta E = 0.358 ev

and thermal energy is kT = 0.1725.

hence all 100 molecules will remain in ground state at v=0, no further possibilities to find electrons in first, second excited states.
The Energy for simple Harmonic OsGilletor, for et the vibrational energy level v, and fundamental frequency o is given as o E = 1V+) nu reke V=2123 -- ele vis vibrational level, Ey is vibrational energy for level v h is plank constant d is fundsmental frequency . for transitions v=o to V=1 we get fundamental frequency of vibrations as Ev=ho ((1+1) - (0+1)]. Ex= ho [ 3 - 1 / 1 = nu Joules - in order to represent equation ② in cmt energy terms Called specroscopic energy term as T = ware (Fundamental vibretiovel) Frequency spacing between Energy level Evil-Ey = SE = 2889 cil Now Thermal Energy - k7 - @ K is soltzman constant, T is absolute temp. thermal energy = KT: 1.38X10 X 2000 K KT = 2.76X1020 goules - convert thermal energy in Joules to appl election valt: 2.76X1020 Joules = 2:1681020 elepon volt 1.6x1519 Thermal energy = 1.725 x10 [0.1725 ev -0 Convert spacing se from cal to ev 8066 Cyt = 1 er ► 2009 Copy : L X 2899 ev wibyoyd SE2 energy spacing I Here TKT <AE L that is thermal Energy is lesser than spacing between level energy rince Most of the 100 Molicule will be et ground state, 8066 01358 ev