Interpretation:Thewave number for C-C stretching vibration needs to be determined, given that vibration for C=C is 1640 cm-1.The wave number for carbon -carbon triple bond needs to be determined wherein the k is appropriate multiple of carbon-carbon double bond.
Concept introduction:
There is large variance in force constant with small differences in bond length. The wavenumber is inversely proportional to square root of reduced mass. Hence, when there is increase in reduced mass, there is decrease in wave numbers.
Answer to Problem 4E
The wave number for C-C bond is 1159.6 cm-1 and stretching frequency of C-C triple bond is 2009 cm-1.
Explanation of Solution
The relation between wave number and reduced mass is depicted in equation
Where
Computing for reduced mass, the equation is
Where
Substituting
From equation (1), all the factors are constant except reduced mass and the reduced mass is inversely proportional to square root of reduced mass.
Where,
But given that
It is known that force constant for C-C triple bond is three times that of C-C single bond.
Hence, computing for C-C triple bonds.
For triple bond, the equation is
Hence, the stretching frequency of C-C triple bond is 2009cm-1.
Thus, the wave number for C-C bond is 1159.6 cm-1 and stretching frequency of C-C triple bond is 2009 cm-1.
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