What is Energy level: Definition and 140 Discussions

A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be quantized.
In chemistry and atomic physics, an electron shell, or principal energy level, may be thought of as the orbit of one or more electrons around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on farther and farther from the nucleus. The shells correspond with the principal quantum numbers (n = 1, 2, 3, 4 ...) or are labeled alphabetically with letters used in the X-ray notation (K, L, M, N…).
Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the nth shell can in principle hold up to 2(n2) electrons. Since electrons are electrically attracted to the nucleus, an atom's electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a strict requirement: atoms may have two or even three incomplete outer shells. (See Madelung rule for more details.) For an explanation of why electrons exist in these shells see electron configuration.If the potential energy is set to zero at infinite distance from the atomic nucleus or molecule, the usual convention, then bound electron states have negative potential energy.
If an atom, ion, or molecule is at the lowest possible energy level, it and its electrons are said to be in the ground state. If it is at a higher energy level, it is said to be excited, or any electrons that have higher energy than the ground state are excited. If more than one quantum mechanical state is at the same energy, the energy levels are "degenerate". They are then called degenerate energy levels.

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  1. RobbyQ

    I Stimulated Emission & Emitted photon direction

    I always understood that a photon of correct wavelength would raise the energy level of an electron (which is the case) But reading about lasers and stimulated emission I read the following where the electron drops a level upon absorption:- "A photon with the correct wavelength to be absorbed by...
  2. H

    Degeneracy of the energy level

    Energy of the One-dimensional box: ground state: En = (n^2*h^2) / (8mL^2), where n=1 twice the ground state: 2* En = 2 [(1^2*h^2) / (8mL^2)] Energy of the Three-dimensional box: En = (nx^2 + ny^2 + nz^2) *h^2 / (8mL^2) = 2 (1^2*h^2) / (8mL^2) As stated, twice the ground state energy of one...
  3. N

    B Energy needed for electron's change in energy level in an atom

    Textbooks always give an explanation for why electrons move between energy levels in atoms with an explanation something like this: 'An electron can jump to a higher energy level if it absorb's energy which exactly matches the difference between final and initial energy level'. My question...
  4. Adams2020

    What is the recoil energy of a nucleus produced in its first energy level?

    Table: To solve, using the conservation of energy: E0=(m(deutron)+m(16O)-m(17O)-m(p))c^2 so: E0=(2.014+15.994-16.999-1.008)931.5=0.93 MeV. so using the conservation of energy: 14.95+0.93=16.62+0+E' E'=- 0.74 MeV But the energy sign has become negative. I also calculated for the first excited...
  5. E

    Definition of energy level width

    First, it is easy to see that n=4 after the collision because: E_1=-13.6\frac{1^2}{1^2}eV=-13.6eV E_4=-13.6\frac{1^2}{4^2}eV=-0.85eV E_5=-13.6\frac{z^2}{5^2}eV=-0.544eVBut, I never saw a definition for the width of an energy level. I tried to use something I saw online that said it was...
  6. WMDhamnekar

    MHB Molecular orbital theory question about energy level diagrams

    Hello, The sigma $(\sigma)$ molecular orbitals are symmetrical around the bond-axis while pi $(\pi)$ molecular orbitals are not symmetrical. For example, the linear combination of 1s orbitals centered on two nuclei produces two molecular orbitals which are symmetrical around the bond-axis. Such...
  7. Adrian Tudini

    Energy level diagram of a chemical reaction

    Hi For a personal project, has the energy level diagram of the below reaction been derived? Voltage Applied4B+2LiNO3+C ------------->B4C+2LiNO2+O2 Thanks,
  8. A

    Partition function of 2 bosons in two energy level 0 and E

    For 2 bosons each of which can occupy any of the energy levels 0 and E the microstates will be 3 0 E a a aa - - aa the partition function is therefore $$z=1+e^{-\beta E}+e^{-2\beta E}...(1)$$ Another approach to do.. The single particle partition function is $$z=1+e^{-\beta E} $$...
  9. LordWhiplash

    I Why is the lowest energy level close to the center?

    While studying photon emission, I noticed that I never really understood why the higher energy level is farther from the center of the atom. To me it seems counterintuitive, because usually the forces of attraction are greater at shorter distances, which would imply a higher energy consumption...
  10. F

    I Why does the energy level of an electron in an atom have a width?

    Electron in atom at higher level(excited state) of energy has tendency jump to lower level of energy.Then the state of electron is unstale,so there is uncertainty in energy of the electron(the level of energy has a width).What cause the level being a band of energy but not a thin line of...
  11. M

    A Qubit Energy Level Required to be Unevenly Separated

    I been reading up on quantum computers and in particular ones based on quantum harmonic oscillators. In all the articles, I have come across they mention a regular, linear LC oscillator cannot be used for a Qubit because it's energy levels are evenly spaced. Therefore, they use a non-linear...
  12. Haynes Kwon

    I Boltzmann equation and energy level occupancy at infinitely high temp

    Let's look at the Boltzmann equation $$ \frac {p_{i}} {p_{j}} = e^{\frac{E_{j}-E_{i}} {kT}},$$ and take infinitely high temperature, the RHS becomes 1. I interpreted that this means every energy level is occupied by equal number of electrons. But if T is high enough, wouldn't the hydrogen atom...
  13. S

    Can Electrons Carry Infinite Energy?

    Are electrons limited to how much energy they can carry(if that term can be used)?
  14. F

    Can a photon with energy greater than energy level difference of atom.

    Can a photon with energy greater than energy level difference of atom be absorbed by atom?Is there any case in that photon share a part of energy for atom and keep other part of energy for itself?
  15. J

    I Mass for solving the nuclear energy level

    Hi all, I'm trying to solve a problem of finite square well for the ##s## states graphically. The task is to find energy levels and wavefunctions of proton in a spherically symmetric potential, first for deuteron then ##^{48}Ca##. What makes me confused is the mass. For deuteron, the mass used...
  16. C

    Can atoms have Vibrational and Rotational energy levels?

    I found one answer somewhere else in the internet, It specified there that atoms cannot have rotational and vibrational energies since they don't have a point on them that will allow the atom to be rotated or vibrated. However , that answer did not suffice so I ask the same question here.
  17. M

    Why Use Nuclear Charge In Finding Energy Value of Singular Electron?

    My Textbook says this is the formula to find energy values for electron shells: $$E_{mol of electrons} = \frac{-1312kJ}{n^2}$$ where $n$ is in electron shell number But when we divide by 1 mol to get the energy value for each electron we get $$E_{electron} = \frac{-2.178 \cdot 10^{-18}}{n^2}...
  18. Edge5

    I Does spin orbit coupling cause the split in the energy level of the electron?

    Hi, As far as I understand spin orbit coupling is the interaction between proton of atom and electron. Proton's motion(from the frame of electron) around electron creates magnetic field. Hence electron experiences magnetic field. Does this magnetic field produces a Zeeman effect which cause...
  19. E

    First order perturbation energy correction to H-like atom

    Homework Statement Real atomic nuclei are not point charges, but can be approximated as a spherical distribution with radius ##R##, giving the potential $$ \phi(r) = \begin{cases} \frac{Ze}{R}(\frac{3}{2}-\frac{1}{2}\frac{r^2}{R^2}) &\quad r<R\\ \frac{Ze}{r} &\quad r>R \\...
  20. Physics345

    Energy level Diagram relating to SP3 hybridization

    Homework Statement Experimental evidence suggests that the nitrogen atom in ammonia, NH3, has four identical orbitals in the shape of a pyramid or tetrahedron. a) Draw an energy level diagram to show the formation of these hybrid orbitals. (hint: No electron promotion is required) b) Name...
  21. G

    B Spontaneous increase in energy level

    i know there is a certain probability for an electron to fall to a lower energy level,without an exciting event,like a collision. Is the reverse also true I.e that a electron could jump to a higher level,without absorbing any extraneous energy..if so are the lifetimes in the new state the same...
  22. L

    Determining which energy level transfers cause peaks in x-ray spectra

    Hi all, I'm wondering how, for each peak in an x-ray spectra from a material (and using a crystal analyser), it is determined which energy level jump the peak corresponds to? How would you figure out the correct value of n to substitute into Bragg's Law to find the energy of the beam? Thank you!
  23. MARX

    BEISER MODERN PHYSICS Rotational Energy Level

    Homework Statement The rotational spectrum of HCl contains the following wavelengths: 12.03 10 5 m 9.60 10 5 m 8.04 10 5 m 6.89 10 5 m 6.04 10 5 m If the isotopes involved are 1H and 35Cl, find the distance between the hydrogen and chlorine nuclei in an HCl molecule. Homework Equations E...
  24. D

    I How Does Rubidium's Electron Spin Affect Its Energy Levels?

    Hello everybody, while I tried to understand the Rubidium level scheme, I realized that I have some issues concerning the energy levels in general... If in addition to the orbital Momentum the spin momentum of an electron is considered for example the p level splits to the 2P1/2-level and the...
  25. barryj

    I Electron energy level values

    Consider hydrogen and helium. Both have electrons in energy level 1. When the electrons move from level 1 to a higher level, are the energy quantum the same for the electrons in hydrogen as in helium? If so, then how can one distinguish hydrogen from helium by observing the emitted light...
  26. J

    I Calculate the energy of the electron in a non-H like atom

    Hello mates. I was doing some research about Rydberg atoms, and I came up with this question: what's the energy of an electron in n energy level in an atom which is NOT hydrogen-like, that is, an atom with more than 1 electron? How can we calculate it? What if the electron we are studying is in...
  27. Wrichik Basu

    B Question in Franck and Hertz Experiment

    My book gives the following graph for current vs accelerating potential for Franck and Hertz experiment (used to prove existence of discrete energy levels in atoms) using Mercury vapours in the tube: The book then writes: "Actually, atoms have more than one excitation potential and also an...
  28. A

    I Change in electron energy level and photon emission....

    Hi all, This is likely a naive question, following up on something @vanhees71 posted some time ago in another thread: My question is the following - if we take an electron that has, for example, absorbed a photon, is the portion of the wavefunction representing the electron in a lower energy...
  29. Arman777

    I Why CERN Energy Level Seems Low?

    I heard that Cern can give particles energy up to ##14TeV## which its like ##2.2430 × 10^{-6}##joules.But it seems so low energy...Why can't we give more energy ? What am I missing Thanks
  30. allanwinters

    Grade 12 chemistry homework help -- 2n^2 electrons possible in each energy level

    Homework Statement A classmate says "Since there are 2n^2 electrons possible in each energy level, and the atom with the greatest number of electrons has 118 electrons, that must mean that u is the highest possible value for n, because a value of 7 gives 2n^2 = 98 nad a value of 8 gives...
  31. S

    I Energy Level Change in Adiabatic Reversible Process

    Hello, I am currently trying to get my head around the concept of entropy. One way to understand it is that it can be related to the amount of available energy levels in a system. From what I read, the availability of energy levels in a system: 1) increase with an increase in the system...
  32. B

    Two energy level system calculate average occupancy

    Hi! I need help with the following question: A system has two energy levels, ε and ε1 that can be occupied by fermions (spin=1/2) that are non-interacting from a reservoir at temperature T and chemical potential μ. Compute the avarage occupation number of the state with energy ε. I have...
  33. NaiveTay

    I Can a Photon be Absorbed Without the Exact Energy Level?

    In my education of QM, I've heard countless times how energy is quantized by Planck's Constant, and how radiation is only emitted and absorbed in these discrete steps. Recently I've heard that that's not the full picture of energy, and I was hoping you could draw some clarity for me. In...
  34. DetectiveT

    What radiation detector can tell energy level?

    Hello everyone. Is there a type of radiation detector that can tell the energy level? I have a basic understanding about Geiger counter and Scintillation counter, they seem only tell the incident particle number. The testing environment may contain Thorium series, Uranium series and Actinium...
  35. C

    Equation for the energy of an electron

    Hello, I would like to thank all of the contributors on this site. You have helped me in more ways than I can count. I am struggling with the following concept and was wondering if anyone could clarify this. As the electron gets further away from the nucleus, its energy increases. This makes...
  36. ptownbro

    Electron Energy Level Fall at a Given Wave Length

    1. Homework Statement An electron in the H atom falls from n=(?) to n=3. The wave length of the emitted photon is 1100 nm. From what level did the photon fall? Homework Equations Used the following to get the Energy. w = c / v E = h * v E = h * (c/w) w = lambda (couldn’t figure out how to...
  37. ptownbro

    Energy release and levels during electron transition

    Homework Statement Been looking but can't seem to find any comprehensive help on this. In the Hydrogen atom, what energy is associated with these electron energy transitions: a) N = infinity to N=2? b) N = infinity to N=3? c) N = 4 to N=2? d) N = 5 to N=6? I don't have any relevant formulas...
  38. T

    Prove that the nth energy level of atom has degeneracy n^2

    Homework Statement Prove that the nth energy level of an atom has degeneracy equal to n^2. Homework EquationsThe Attempt at a Solution I was thinking of using the sum from n=1 to N of n = N(N+1)/2 but my professor said i needed to change that equation up a bit to be able to show this. I was...
  39. Tonia

    Where is the fifth energy level in relation to the fourth?

    Where is the fifth energy level in relation to the fourth energy level? Well, it shows that energy level five is at n= 5 and energy level four is at n=4 away from the nucleus, so that means that the fifth energy level is at the 16th orbital and energy level four is at the 25th orbital?? I am not...
  40. mss90

    Value of n for the energy level transition that produce lamb

    Homework Statement A wavelenght of 410.2*10^-9m is emitted by the hydrogen atom in a high voltage discharge tube. what are the initial and final values of the quantum number n for the energy lvl transition that produces this wavelength? Homework Equations 1/(lambda) = R * (1/2^2 - 1/n^2)...
  41. 1

    Prob of part being in Lowest Energy Level after Potential Change

    First off sorry for the badly worded title. 1. Homework Statement Beginning of Question: Consider a single quantum particle of mass M trapped in the infinite square well potential, V(x), given by V(x)= 0 if 0 < x < L infinity otherwise The wave function for a particle in the n-th...
  42. CAH

    Electron-Electron Interaction & Photon-Electron Interaction?

    I learned that photons can exite and ionize electrons in an atom, bring them to higher energy level etc. However I've seen a few questions on electrons bombarding electrons in an atom and exiting the orbital electrons to higher energy level. Is this the same as the photoelectric effect when...
  43. A

    Polarization and energy level transitions

    Hello. What is troubling me is I can't stabilish a connection. and it seems to be it should exist, between the polarization of a material by displacement of the electron cloud and energy level transition in a molecule or solid. When an electric field is applied to a material, the "electronic...
  44. Z

    How to find the energy level if a three state system

    I'm having trouble figuring out how to derive a Hamiltonian for a three state system. I know how to for two state system but for a three state I don't know what vectors I could use to derive the operator. Could someone explain how to do it and give a link to somewhere I read about it
  45. K

    Notation on energy level for atoms

    Hi there, I am reading an introduction for atomic physics. In one section, it introduces the energy levels for Rubidium and there are some labels like F=1, F=2 etc. shown next to the fine structure of a level . Also refer to...
  46. T

    Double bonds and energy level

    I am curious, for linear conjugated molecules, for example, those with double bonds as in 1, 3-butadiene or 1, 3, 5-hexatriene, how are their double bonds (suppose # of double bonds = N) related to energy levels (n)? From what I gather, those with two double bonds have energy level n =2 and...
  47. O

    Calculating Initial Energy Level for Emitted Photons

    Homework Statement Using the energies, determine from which initial energy level (n) the electrons decayed when it emitted photons at each of these wavelengths. Homework Equations E = - \frac{ me^4 }{ 8\epsilon_0^2h^2 }\frac{ 1 }{ n^2 } Delta E = E_f-E_i= - \frac{ me^4 }{ 8\epsilon_0^2h^2...
  48. L

    Confusion Over Same Energy Level Transitions

    Homework Statement This is more of an understanding issue than a homework problem, but if I don't understand, I can't prepare for homework. With regard to energy level transitions, the text states almost as an afterthought that "Transitions between the same energy levels always produce the...
  49. A

    Individual states of a particular energy level

    In thermodynamics what is meant by "the number of individual states that belongs to one energy level"?My current understanding is that different individual states of one energy means a system with different pressure,volume and temperature that belongs to a particular energy level? please can...