The concept that an electron can only absorb a specific amount of energy from light is derived from the principles of quantum mechanics. In quantum mechanics, particles such as electrons are described by wave-particle duality, meaning they can exhibit both particle-like and wave-like properties.
When light interacts with matter, it does so in discrete packets of energy called photons. Each photon carries a specific amount of energy, and when it interacts with an electron, it can transfer its energy to the electron. However, for the electron to absorb the energy, it must undergo a transition from one energy level to another within an atom or a molecule.
According to the Bohr model of the atom, electrons exist in quantized energy levels, or shells, around the nucleus. The energy levels are represented by specific values, and an electron can only occupy these energy levels or transition between them by absorbing or emitting discrete amounts of energy. The energy of the photon must match the energy difference between the initial and final energy levels for the electron to absorb it.
The specific energy levels and the corresponding energy differences are determined by the characteristics of the atom or molecule, such as its atomic number and electronic structure. Each atom or molecule has a unique set of energy levels, resulting in the absorption and emission of light at specific wavelengths or frequencies, forming a characteristic spectral pattern.
This phenomenon is observed in spectroscopy, where scientists study the interaction of light with matter. By analyzing the absorption and emission spectra of different substances, it is possible to determine the specific energies that electrons can absorb and the corresponding energy transitions they undergo.
So, the understanding that an electron can only absorb a specific amount of energy from light arises from the quantized nature of energy levels in atoms and molecules, as described by quantum mechanics.