I have tested paracetamol using UV-Vis characterization and the result of paracetamol maximum wavelength is 243 nm, the result is same with the literature. But, why does paracetamol have a maximum wavelength (λmax) at 243 nm?
Saeed Ayaz Khan why is paracetamol only detected in the UV region (under 400 nm) not in the visible region (above 400 nm)? If paracetamol is also tested above 400 nm, will there be another peak or will it just be flat peak?
Your question is not an easy one to answer. Determining the transition energies between the ground and excited states of a molecule involves complicated computations, but looking at the structure of paracetamol and having some experience with other molecules, I am not terribly surprised that its first absorption band is around 243 nm.
It can be helpful to think about the electronic energy in terms of something you learned about in general chemistry and thought had no real importance -- the "particle in a box." If you remember, as the box is lengthened, the energy of the waves that can fit into the box decreases; the wavelength (λ) increases and E = hc/λ.
For a molecule, the "box" is the total length of connected pi conjugation. Electrons have wave-character and the wavelength is determined by the distance they can span. For example, butadiene (~217 nm) will have a lower energy (higher wavelength) absorption band than any form of butene (~180 nm), since it has 4 carbons connected through pi bonds instead of 2. While linear examples of molecules are easier to understand in terms of the particle in a box, the same holds for cyclic systems. In terms of the first absorption band wavelength, anthracene (~375 nm) > naphthalene (~286 nm) > benzene (~255 nm).
So when I look at paracetamol, I see a single ring that may be conjugated to the other double bond through the nitrogen lone pairs. The degree of conjugation depends on bond rotations, and that depends somewhat on the solvent. There are a lot of complications that limit the usefulness of the particle in the box picture, but I think it's the best way to start looking at absorption and fluorescence. To really get good estimates of the energies, complicated computations (time-dependent density functional theory is what I think is considered the best, but I'm not an expert) are required. They begin with a geometry-optimized molecule and determine where electron density is for ground and excited states.
I only looked at this webpage to get the absorption wavelengths, but it looks like there is good information about what functional groups can do if you're curious: https://www.shimadzu.com/an/service-support/technical-support/technical-information/uv-vis/uv-ap/apl/index.html
The rabbit hole is deep here, and it gets mathy fast. Hope this is a good start for you.