What is Energy levels: Definition and 276 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. alemsalem

    Can internal energy levels of atoms affect chemical potential of ideal gas?

    μ/T represents the change in entropy if we change the number of particles,, so according to the fundamental assumption of statistical mechanics μ/T should tell us about the tendency of two systems to exchange particles... but I am having a hard time imagining how rotational or vibrational...
  2. G

    Missing something pretty simple in counting energy levels?

    Homework Statement Determine the no. of energy levels with different values of total spin for a system of N particles with spin 1/2 The Attempt at a Solution Let f be the no. ways to get a z projection of spin, then f(\sigma )=Binomial(N,\frac{1}{2}N + \sigma) Where Binomial(a,b) is a chose b...
  3. G

    Exchange splitting of energy levels of a system?

    Exchange splitting of energy levels of a system?? Hey guys, I was just reading my QM book and came across this; Homework Statement Determine the exchange splitting of energy levels of a system of two electrons, regarding the interaction of the two electrons are a perturbation. My...
  4. C

    Energy levels hydrogenic atoms

    I don't get why for hydrogenic atoms the 2s and 2p orbitals have the same energy. i do get it mathematically, but I am thinking that the fact that there are angular nodes in 2p and not in 2s MUST affect the energy!
  5. C

    Is photon emission possible without electrons changing energy levels?

    Does molecular vibrational transition and consequent emission of infrared radiation involve electrons changing energy level? In wikipedia, about vibronic transitions it says "Most processes leading to the absorption and emission of visible light, are due to vibronic transitions. This may be...
  6. J

    Energy levels and quantum state

    Would anyone be able to explain s,p,d,f in detail without using complex math? Also quantum states such a m,l etc. or link me to a site/paper that does? thanks
  7. F

    Rare-earth energy levels from LS coupling

    Hey all, Is there a way to rank the energy levels of a rare-earth ion in order of increasing energy just from the spectroscopic terms? Nd3+ has an electron configuration of [Xe]4f^3, which produces energy levels such as 4I, 4F, 2H, 4S, 2G, 4G, 2D, etc from the electrostatic interaction...
  8. binbagsss

    Quick Uncertainty Problem - atom energy levels

    Two quick problems, not sure whether the 2 are related or not: 1) The question is: A sodium atom in one of the states laveled 'lowest excited lvels' remains in that state, on average, for 1.6 x 10^-8 s before it makes a transition to the ground level, emitting a photon with wavelength...
  9. N

    Given a potential, qualitatively deducing the energy levels?

    Given the basic result that the harmonic potential well has the energy levels it has, are there ways to convincingly deduce the qualitative properties of the energy levels given a certain potential well? Take for example a Morse potential, is there a way to deduce (vague if need be, exact if...
  10. D

    Molecular Orbital energy levels

    Hi everyone I'm currently studying the MO theory and ran into some trouble understanding orbital energy levels. As I have previously read, σ bonds are stronger than ∏ bonds, therefore are lower in orbital energy. However, from the MO theory, the σ2p orbital is actually higher in energy than...
  11. D

    3D Schrodinger Equation of a Wire for Energy Levels - Quantum Physics

    Homework Statement Given a wire with length a and square base b x b (where a >> b), show that the first 1700 (approximately) levels of the electron in the wire are identical for the one dimensional box, when a = 1m and b = 1mm. Homework Equations I know that the allowed energies of...
  12. G

    Energy levels in Hydrogen - derivation

    Homework Statement We know that: E=<\psi|H|\psi> where H=-\frac{\hbar^2}{2m} \nabla^2 - \frac{Ze^2}{4\pi\epsilon_0 r} and \psi=R(r)Y(\theta, \phi) with R(r)=\frac{1}{\sqrt{(2n)!}}(\frac{2Z}{na_0})^{3/2}\left(\frac{2Zr}{na_0}\right)^{n-1}e^{-Zr/na_0} If I want to find the energy, do...
  13. A

    Hydrogen's energy levels don't depend on l or m because

    Homework Statement Why doesn't the energy of the hydrogen atom depend on quantum numbers l or m? Homework Equations E = (Z^2) 13.6 eV / n^2 The Attempt at a Solution Regarding l: I know that it has to do with the inverse-square law between the distance, r, of the e- and the...
  14. O

    Energy levels of nucleus in emitting radiation in MRI

    Hi experts please explain energy levels of nucleus in emitting radiation in MRI
  15. T

    Infinite number of energy levels available to an atom

    I'm confused about something. If there are an infinite number of energy levels available to an atom, how and why would an ionization need to take place? The electron always has another energy level to occupy once its energy has been raised.
  16. A

    How emissions for a spectra provide evidence for energy levels in a atom?

    Explain how data from emissions spectra provide evidence for discreet energy levels within the atom?
  17. A

    Why do atoms emit discrete frequencies of light?

    Homework Statement Why are electronic levels present for an atom? What is the need for differentiating energy levels?
  18. B

    Rotational and vibrating energy levels - find energy separation

    Homework Statement The equilibrium separation of the atoms in H35CI equals 1.27 x 10-10m. Calculate the energy separation between adjacent lines in the rotational-vibrational spectrum Homework Equations E = (n + 1/2)h\omega + h2/ 2I * l(l+1) I = \mur02 \mu = m1m2/ m1 + m2 The...
  19. D

    Can anyone explain energy levels of an Atom?

    Now, from what I understand, Bohr's model of the atom is outdated and flawed. But whenever I imagine energy levels, it is the Bohr's model that comes to mind. Do electrons really orbit around the nucleus? I would assume because of classical physics, even though the electron can be on any portion...
  20. phinds

    Some energy levels ruled out for Higgs

    http://www.bbc.co.uk/news/science-environment-14258601
  21. Q

    Orbital Blocks and Energy Levels

    Ok, I know that the S, P, D, and F represent blocks (groups of elements) on the periodic table. I know that the numbers represent rows on the periodic table. But what about the arrows? What's with the business of "increasing energy"? Why are the arrows slanted...
  22. U

    Nuclear Shell model, how do we know energy levels?

    One of my 'course aims' is to be able to classify the shell model energy levels in terms of quantum numbers l and n and explain how magic numbers arise. I'm using this to help to understand it as well as lecture notes. http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html I know...
  23. E

    Exploring Energy Levels and Spin: Questions on Bosons, Fermions, and 2S+1

    I have a couple questions related to different energy levels and spin. Our professor taught us one way and the TA a different in our review session. We tried to hash it out in class but had to move on. I suspect both the TA and prof were talking about different things - or maybe stuff we won't...
  24. E

    Particles with Spin in a Box - Energy Levels

    Homework Statement This is a two part problem. I think I am pretty close, but I'm quite understanding it. Which sucks because this is probably an extremely easy question.:frown: I have five particles in a box with S spin. I am to find the ground state of the five particles if they have...
  25. A

    Energy levels for two particles in infinite potential well

    problem is: (a)write down the spatial or orbital for two-non interacting particles, with the same mass, in a one dimensional well, where the potential energy is zero for 0<x<2a and infinite anywhere else. (b)What are the energies of the four lowest energy levels for the system in units of...
  26. A

    Kinetic energy during energy levels

    Homework Statement hi this is a problem that puzzles me. it goes like this: energy/10–18 J ionisation level 0.0 level D level C level B ground state A –1.9 –2.1 –2.4 – 4.6 An electron with kinetic energy 2.6 × 10–18 J collides inelastically with an electron in the ground state...
  27. L

    Contribution to the heat capacity of vibrational energy levels.

    Homework Statement The carbon-dioxide has nondegenerate vibrational energies εr=(h/2π)ω(r+1);r=0,1,2..., where ω=(1.26*10^14)s^-1. What is the contribution of these vibrational modes to the molar heat capacity of carbon-dioxide gas at T=400K? Homework Equations...
  28. Z

    How to find energy levels in doped silicon

    Homework Statement This is part of a much larger problem, but I'm stuck on trying to draw an energy band diagram for doped silicon and I'm wondering if it is possible for me to find the energy levels ( E_c, E_v, E_f, and E_i ) in a doped semiconductor knowing only the concentrations? This...
  29. B

    Energy levels for a different plancks constant

    I am writing an essay about what would happen if Planck's constant changed to a much larger number. What I am having a hard time with is the discretization of energy levels for bound system... how would that change if Plancks constant was larger? Thanks for all the help in advance.
  30. V

    Quantized Energy Levels: Understanding the Basis of Schrodinger's Equation

    If you solve Schrodinger's equation for a particle in a box you find the solutions to be sines and cosines. The boundary condition that the wave function must go to zero at the edges of the box then leads to the need for an integral number of wavelengths and in turn quantization of energy. I...
  31. A

    Energy Levels: What Happens if First Level Contains More Than 2 Electrons?

    Hi every body and how do you do first sorry of my weak language because I'm new physical Researcher at KACST & I'm learn English now before go to master degree so my physical question is about the number of electrons in the first level of energy levels we know the the first level can't...
  32. T

    Why are photons emitted when electrons drop energy levels

    Hi everyone, So I'm doing some research on fluorescence and I'm puzzled. I understand that running a current through fluorescent gasses like neon cause the valence electrons to jump up an energy level, and I understand that photons are emitted when they fall back down into their default...
  33. nomadreid

    Zeroes of zeta function as energy levels?

    In "A Prime Case of Chaos" (http://www.ams.org/samplings/math-history/prime-chaos.pdf), the author states that "Physicists ... believe the zeroes of the zeta function can be interpreted as energy levels..." I have two problems with this: (1) the non-trivial zeroes of the zeta function are...
  34. nomadreid

    Can Complex Numbers Really Be Interpreted as Energy Levels in Physics?

    In "A Prime Case of Chaos" (http://www.ams.org/samplings/math-history/prime-chaos.pdf), the author states that "Physicists ... believe the zeroes of the zeta function can be interpreted as energy levels..." I have two problems with this: (1) the non-trivial zeroes of the zeta function are...
  35. D

    Are Degenerate Energy Levels the Same as Ground States in Quantum Mechanics?

    Hi... I'm having a little trouble understanding this concept. An energy level is a level where fx. electrons can be in. Ground state, 1st excited state etc., right ? So if I'm not mistaken, a degenerate state is when two or more different quantum states (Fx. electrons) are in the same...
  36. W

    Boltzmann Factor/predicting energy levels

    I'd like to just preface this by saying I'm a non-science major in a science course. The professor mentioned we might need another textbook besides the ones for this particular class. Unlike all of the science/engi majors in the class, I don't have it. Homework Statement Using the...
  37. T

    Do vibrational energy levels decay?

    Hi, I was just wondering if the vibrational energy levels in molecules decay, emitting a photon? or by some other mechanism? For example, if a laser is used to excite a vibrational mode (Like that in Stokes-Raman Scattering) from say v = 0 to v = 1 state. Will the molecule remain in the v...
  38. R

    Total energy levels of the electron and rest energy

    hi, the following question is extremely important so please reply! in an atom, the energy levels of the electrons are negative and the velocity of the electron increases when the energy decreases. however, this cannot be the total energy(in relativity) because it does not includes the...
  39. M

    Quantum Energy levels in atomic, molecular, nuclear and solid state physics

    Homework Statement Greetings everyone I have been been asked to write a 10 page essay on Quantum Energy levels in atomic, molecular, nuclear and solid state physics. My problem is that this is such a huge topic and my knowledge of quantum energy levels and solid state physics is limited...
  40. C

    Energy levels and line spectra

    I read that each line on a line spectra for an element represents an energy level. Hydrogen only has 1 electron which is in the first energy level so why are there so many lines on the H line spectrum?
  41. alemsalem

    Energy levels of the HE4 nucleus

    what i mean is could it be possible for an alpha particle to acquire energy (by collision or from emission) and subsequently emit a gamma ray?? or does only have one (ground) state??
  42. R

    Calculate 1st 3 Energy Levels for Electron in Quantum Well

    Homework Statement Calculate the first three energy leveles for an electron in a quantum well of width 10Angstrom and infinite walls. Homework Equations En=\frac{n2pi2(hbar)2}{2mL2} The Attempt at a Solution m=9.109E-31Kg L=10E-10m hbar=1.055E-34 En=n2*6.032E-20 My problem...
  43. S

    Infared WAvelengths in transition through energy levels

    Homework Statement How many transitions involving the hydrogen energy levels shown correspond to photons of infrared light? The infrared range is less than 1.8 eV Homework Equations Paschen Lines = Infared wavelengths The Attempt at a Solution I thought that since Paschen lines =...
  44. C

    Why Do Helium Atom Energy Levels Split in Different Interaction Scenarios?

    Homework Statement I have having difficulty explaining the splitting of helium atom energy levels for three different cases: 1)Coulomb interaction is ignored 2)Coulomb interaction is present but exchange interaction is neglected 3)Coulomb and exchange interactions are present The Attempt...
  45. I

    Exploring Degeneracy in Energy Levels and Quantum Numbers in a 3D Box

    okay this isn't exactly me asking how to solve a question but just to verify the theory in my head. i need to calculate the 4 lowest energy levels for a 3d box (that has sides (2a,a,a)) and show all the quantum numbers (i imagine it means the x,y,z components of n, l, ml) and give the...
  46. W

    Energy levels of carbon atom electrons

    Homework Statement Consider a neutral carbon atom that has six electrons orbiting the nucleus. Suppose that five of the electrons are in their lowest states,but the sixth is in a very high state. Why might the energy levels for the outermost electron be similar to those for the single...
  47. M

    Atomic Energy Levels in the Presence of a Magnetic Field

    Homework Statement In the presence of a magnetic field, the energy of an atomic energy level is changed by the quantity: Emag=g\muBBM (i) Expain the meaning of the terms in the expression. (ii) Into how many levels is the ground state of the sodium atom split? (iii) For each...
  48. P

    Bhor's rule breaking energy levels

    Bhor's rule breaking "energy levels" when Ernest Rutherford's model of planetary system to explain the atomic structure, he was forced to have the regret by the fact that "accelerated charges dissipate their Kinetic energy into EM radiations." Bhor tried to avoid it.So he engaged the idea of...
  49. K

    Energy difference between energy levels with same n

    Homework Statement I am somewhat confused about calculating the energy difference between different energy levels with the same principal quantum number (n). Eg. one of the questions that I have requires me to work out the energy difference between 23P2 state and the 23S1 state.Homework...
  50. S

    Can Electrons Exist at Extreme Distances from Their Atomic Nucleus?

    Are there (available) energy levels of an electron say, at a distance 1m, or 100m or 1km away, and near the moon and beyond that belongs to an atomic nucleus on Earth ? If yes, then why does it prefer to be within the 10^-10 meter distance from the nucleus ? Sridhar
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