Allowed energy states are the specific discrete energies electrons can occupy in quantum systems without breaking quantum rules. In Principles of Physics III, they explain atomic levels, bands in solids, and how electrons conduct electricity.
Allowed energy states are the energy values an electron can actually occupy in a quantum system such as an atom or a crystal. In Principles of Physics III, this means electrons do not have a smooth range of energies the way a rolling ball does. They are limited to specific states set by the wave nature of matter and the boundary conditions of the system.
In an atom, those states show up as quantized levels. An electron can sit in one level or another, but not in between. That is why an electron cannot have just any random energy inside the atom. The allowed values come from the solutions to Schrödinger’s equation, and only certain wave patterns fit the atom’s constraints.
In a solid, the same idea turns into band theory. When many atoms come together in a crystal, the individual atomic levels split into very closely spaced allowed states. Those states form bands, such as the valence band and conduction band. The space between bands contains forbidden energy states, where no electron state exists for the crystal.
A free electron model treats electrons as if they move through the metal with very little interaction, which makes it easier to see why bands form. The electrons still cannot have arbitrary energies because the finite size of the solid and quantum rules restrict the wave patterns they can form. So even when the picture looks “free,” the allowed energies stay quantized.
This is also why energy changes happen in jumps. An electron moves from one allowed state to another by absorbing or emitting a photon, or by gaining energy through collisions or heat in a material. The exact jump depends on the spacing between states or bands, which is why allowed energy states connect directly to spectra, conductivity, and optical behavior.
Allowed energy states are the backbone of the quantum view of matter in Principles of Physics III. If you know which energies are allowed, you can predict whether electrons stay bound to atoms, move easily through a solid, or need a specific amount of energy to jump upward.
That matters most when you compare materials. In a metal, the allowed states near the Fermi level are available for electrons to move into, so current flows easily. In a semiconductor, the pattern of allowed states and the gap between them controls whether electrons stay in the valence band or reach the conduction band. In an insulator, the gap is large enough that ordinary energies do not move many electrons across it.
The term also gives you a clean way to read graphs and models. If you see a band diagram, you are not just looking at a picture of “electron energy.” You are looking at where states exist, where they do not, and how much energy is needed for a transition. That is the same logic behind absorption and emission lines, electrical conductivity, and the way materials respond to light.
So when a problem asks why a material conducts, glows, or absorbs a certain frequency, allowed energy states are usually part of the answer. They tell you what transitions are possible and what the electron cannot do.
Keep studying Principles of Physics III Unit 11
Visual cheatsheet
view galleryBand Gap
The band gap is the energy difference between allowed states in the valence band and allowed states in the conduction band. When that gap is large, electrons need more energy to jump across it, so the material acts more like an insulator. When the gap is smaller, thermal energy or light can promote electrons more easily.
Density of States
Density of states tells you how many allowed energy states exist at each energy level. Two materials can both have allowed states, but if one has many more states available at a certain energy, electrons are more likely to occupy them. That affects conductivity, absorption, and how the material fills up as electrons are added.
Fermi Level
The Fermi level marks the highest occupied energy level at very low temperature, or a reference energy for electron occupancy in a solid. It helps you locate where electrons sit among the allowed states. In metals, the Fermi level lies inside a band, while in semiconductors it sits in the gap.
forbidden energy states
Forbidden energy states are the energies electrons cannot occupy in a quantum system. They are the complement of allowed energy states, especially visible in band theory. If a problem asks why electrons cannot drift smoothly from one band to another, the forbidden region is the reason.
A quiz or problem-set question usually asks you to identify where the allowed states are in an energy diagram and decide whether an electron can move to a new level. You might sketch a band diagram, label the valence band, conduction band, and gap, then explain whether heat, light, or an applied voltage can produce a transition. In a short-answer prompt, you may need to connect the allowed states to conductivity, saying why a metal conducts more easily than a semiconductor or insulator. If a graph of electron energies is given, the task is often to read the spacing between states and interpret what that means for absorption or emission. The key move is to go from the diagram to the physical behavior of the material.
Allowed energy states are the specific electron energies a quantum system permits, not a continuous range.
In atoms, they appear as discrete levels; in solids, they combine into bands.
Electrons change allowed states by absorbing or emitting energy in a jump, not by sliding smoothly.
The pattern of allowed states helps explain conductivity, absorption, and whether a material behaves like a metal, semiconductor, or insulator.
If a value falls in a forbidden region, an electron cannot occupy it in that system.
Allowed energy states are the energies an electron can occupy in a quantum system such as an atom or solid. In this course, they explain why electron energy comes in discrete levels and how those levels become bands in materials. They are the starting point for understanding conductivity, spectra, and band gaps.
Not exactly. An allowed energy state is any permitted electron energy, while an energy band is a very dense group of allowed states in a solid. Bands form when many atomic levels bunch together, so the two ideas are connected but not identical.
Because electron behavior is governed by quantum mechanics, the electron wave has to fit the system’s boundary conditions. Only certain wave patterns are stable, and those patterns correspond to allowed energies. Any energy outside those solutions is a forbidden state for that system.
They determine whether electrons have nearby states they can move into when energy is supplied. In a metal, available states near the Fermi level let electrons respond easily to an electric field. In semiconductors and insulators, the spacing and gaps between allowed states make that motion harder.