Why an electron can only absorb light if the energy exactly equals the gap between two allowed orbits or shel

why an electron can only absorb light if the energy exactly equals the gap between two allowed orbits or shells?
i have reed this in my chemistry lecture notes but didn't know the reason?

Well, an orbital electron has quantised energy i.e. it can't just take up any energy. You can either just accept this or you can prove it to yourself by solving the Schrodinger equation corresponding to the atom in question, in which case you may need a background understanding of quantum physics. So the orbital electron won't just absorb any energy, but only those energy amounts that cause it to end up with one of its allowed energies. These allowed energies are the gaps between the allowed orbits or shells you mentioned and the energy source in your case is the light.
Hope that helps buddy :)

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But actually shells are less active when they are half filled

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But actually shells are less active when they are half filled

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But actually shells are less active when they are half filled

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Energy is a quantum property. As such, it exists only in multiples of whole numbers. And En - E0 = nhf, where n is that whole number defines the gap in energy levels En and E0; where E0 is the ground level energy before absorbing the photon.

Note that as the number grows, that indicates a higher energy gap. That results in higher frequency photons when the electron snaps back to ground level. So we can actually tell which electron shells are involved in the light emitted when the electrons fall back to where they came from. This is called the Zeeman Effect, something you may get in lab one day.