There is Carbon - Carbon single bond and Carbon - Carbon double bond and Carbon - Carbon triple bond......
To my question ...
Why there is no Carbon - Carbon 4 bond even though Carbon has valency of 4 .
Carbon has a valence of four. It can form four bonds but it only forms compounds with single bonds (alkanes) double bonds (alkenes) or triple bonds (alkynes).
Even the alkynes are unstable. Nearby oxygen and nitrogen form common diatomic molecules, but not with quadruple (or even triple) bonds. The basic answer would have to be that once you have the triple bond, there's no possible quantum orbit that allows one more electron to orbit both nuclei such that the total molecule has a lower energy.
For an electron to orbit both nuclei instead of just one, its orbit length would need to be increased by one wavelength of its wavefunction (raising it to a higher energy level), or the nuclei would need to move closer together (increasing the repulsive electrostatic potential energy between them). That repulsion is inverse square with distance, so the closer you push the nuclei together, the harder it is.
There is no space to accommodate that bond. Think of an alkyne like ethyne. Ethyne has 1 sigma bond and 2 pi bonds. What does this mean in 3D? Well picture 2 basket balls (carbon) with a pipe connecting the two of them, this is your sigma bond. Lets say that the sigma bond is on your y-axis, and that the y-axis is in the plane of your paper. Now lets add a pi bond, this pi bond will be on the z-axis (going up and down). Now we have to add the second pi bond, but they only space available is on the x-axis (coming out and goind back in). It is pretty crowded now and we cannot fit another pi bond between the carbons, that is why you will not see a carbon-carbon quadruple bond.