When an electron absorbs energy from a photon, the interaction occurs at the quantum level and is described by quantum electrodynamics (QED), which is the theory that combines quantum mechanics with electromagnetism.
The energy transferred to an electron by a photon is determined by the frequency (or equivalently, the energy) of the photon. Higher-frequency photons indeed carry more energy compared to lower-frequency photons. This is because the energy of a photon is directly proportional to its frequency, as described by the equation E = hf, where E is the energy, h is Planck's constant, and f is the frequency.
However, it is important to note that the interaction between the photon and the electron is not a continuous process that occurs over a span of time. Instead, it is a discrete event that takes place at a specific point in space and time. In the framework of quantum mechanics, the absorption of a photon by an electron is described by the concept of an instantaneous "quantum leap" or transition between energy levels.
The duration of this interaction is not directly related to Planck time or space. Planck time (t_P) is the smallest unit of time that can be meaningfully defined in the context of current physical theories, and it represents the time scale at which quantum gravitational effects might become significant. The absorption of a photon by an electron typically occurs on much shorter time scales, often described by the concept of the "transition probability" within the framework of quantum mechanics.
Similarly, the interaction does not involve Planck length (l_P), which is the smallest length scale that can be sensibly described in our current understanding of physics. The absorption of a photon by an electron is typically described by the wave function of the electron and does not involve direct considerations of space at the Planck scale.
In summary, the energy transferred to an electron by a photon is determined by the frequency of the photon. The interaction between the photon and the electron is a discrete event that takes place at a specific point in space and time, and it is described by quantum mechanics rather than being directly related to Planck time or space.