# General Modern Physics questions

#### newguy1234

In my modern physics course we learn that different atoms and molecules have a unique set of allowed orbitals where it's electrons are allowed to exist. We then talk about how this corresponds to unique spectral lines emitted and absorbed by the different atoms/molecules. This continues onto what happens if we shine light of the correct frequency on an atom so the photon energy is absorbed and an electron moves to a higher energy level. My confusion lies in the part.

Some people/references describe this by saying a photon comes in with a correct energy (equal to the difference between any two of the allowed orbitals) and actually hits an electron and knocks it to a higher energy level/orbital.

Other people simply say the photon energy is absorbed by the atom (which I assume they mean the nucleus) and this extra absorbed energy is somehow, through some unknown mechanism, communicated to the electron and manifests as the electron moving to a higher energy level.

Maybe the problem arises because neither is what really happens since the electron is not really orbiting the atom. I read but do not fully understand yet, that the electron exists as a probability cloud around the nucleus of the atom. I guess this means solving the Schrodinger equation for the atom (say hydrogen) with the coulomb potential. You get a $$\Psi(x,t)$$ solution which would corresponds to probability distribution for the electron around the nucleus.

Also I was reading in the FAQ section 'do photons move slower in a solid medium'. It talks about the adsorption of an electron by an atom (not and electron so maybe that is the answer?) and how that is not how the question is explained. It says the quantized lattice vibrational modes are what absorb the photons and create the delay through the medium. It also talks how this phonon photon adsorbtion also explains what makes materials/mediums opaque or transparent. I was recently taught that this was because the material had collective allowed energies. If the incoming radiation had an energy lower or higher than these allowed energies the material was transparent and if the incoming radiation had energy equal to allowed energies it would be absorbed and be opaque. Is it safe to say now this this explanation is wrong?

I thank you for taking the time to read through my post. To restate my questions: What moves an electron in an atom to a higher energy level when a photon is used for excitation, does it collide with the photon? and what explains why materials are opaque, translucent, and transparent to different radiation energies. Thanks for your time

#### malawi_glenn

Homework Helper
In the quantum mechanical view, it only exists certain energy levels where an electron can be bound to an atomic nucleus. This is due to the properties of differential equations.

The "quantum motion" of particles are governed by the Schrödinger equation, which is a differential equation for the wave function of the particle. The wave function is the probability density. Now the probability cloud is just what you say it is, it is the solutions to the Schrödinger equations which gives you the allowed states (orbitals or whatever you want to call them).

Now let's look at the properties of differential equations, they have a discrete set of eigenvalues and a set of eigenfunctions, which are orthogonal to each other. Let's apply this to the schördinger equation:
$$H \Psi_m(x,t) = E_m \Psi_m(x,t)$$

H is the hamiltonian, the differential operator. E is the eigenvalue, and Psi is the eigenfunction. So, according to theory of differential equations, the system possesses a discrete set of eigenstates (wavefunctions: probability density distributions) and corresponding eigenvalues (Energy-eigenvalues)

Now let's go on to the interaction with a photon. Without getting into mathematical details on quantizing the electromagnetic field, I can say that you have a small disturbance to your original hamiltonian H, so the new hamiltonian H' = H + V, where V is the electromagnetic 'field' of the photon, a small 'disturbance'.

So now we have a new hamiltonian, with new eigenstates and eigenenergies. And then you can determine those in terms of the old eigenstates, with a method called perturbation theory (which you will learn about later in school).

So then you can calculate that probability that a transition from state 1 goes to a higher state 2 when the incoming photon interacts and 'disturb' the electron. So the mechanism is not unknown, it can be described in quite many ways. Later you will learn how to quantize the electromagnetic field and perform Quantum Electrodynamic calculations.

The most essential is that photons do not 'hit' electrons, like tiny balls.

Now the solids are just like atoms, but they possess energy BANDS instead of levels. So a solid has, just as the atom, energy levels where states exists and thus can absorb photons. If a solid does not have an energy band in the energy region of say visual light, the solid becomes transparent to those wavelengths of light (glass for instance).

#### newguy1234

@malawi_glenn thank you for your reply. I appreciate you taking the time and clearly explaining this to me. Also sorry for posting in the wrong Section originally.

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