Energy levels Definition and 276 Threads

Homework Statement If the first two energy eigenfunctions are ## \psi _0(x) = (\frac {1}{\sqrt \pi a})^ \frac{1}{2} e^\frac{-x^2}{2a^2} ##, ## \psi _1(x) = (\frac {1}{2\sqrt \pi a})^ \frac{1}{2}\frac{2x}{a} e^\frac{-x^2}{2a^2} ## Homework EquationsThe Attempt at a Solution Would it then be...

Homework Statement When an electron in a hydrogen atom makes a transiton between two levels with prinicipal quantum numbers n1 and n2, light is emitted with wavelength of 658.1 nm. If we assume that the energy levels of the atom are in agreement with the Bohr model, what are n1 and n2...

Homework Statement 1D Potential V(x) = mw^2x^2/2, part of a harmonic oscillator. Suppose that the spring can only be stretched, so that the potential becomes V=infinity for x<0. What are the energy levels of this system? Homework EquationsThe Attempt at a Solution I argued my way though this...

1. The problem statement, all variables, and given/known data After thinking over your beloved but erratic instructor’s lectures on the Bohr model of the atom, you come to the sad but inevitable conclusion that he has, yet again, lied to you. You have been taught that to make an electronic...

In the 'Particle in a box' system, with the well being extremely narrow, why does the particle path have to follow certain energy levels compared to the classical system? Thanks in advance.

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...

Hey, I just had a quick question about using hamiltonians to determine energy levels. I know that the eigenvalue of the hamiltonian applied to an eigenket is an energy level. H |a> = E |a> But my question is if I am given an equation for a specific Hamiltonian: H = (something arbitrary) And...

Homework Statement A system has three non-degenerate energy levels with energies 0, ε, and 2ε. a) Calculate the entropy of the system if the three levels are populated by two distinguishable particles such that the total energy is U=2ε. b) Calculate the entropy of the system if the three...

From statistical mechanics in zeemansky's book . He states that it's easy to see that for a closed system the no. Of degenerate states ##g_i## for energy level ##E_i## is greater than the number of particles ##N_i##occupying that energy state. I can't find a mathematical proof for it. Can I...

I've just started with statistical mechanics and arrived at the part where they relate entropy to the number of microstates for a given system. The derivation starts of by adding an amount of heat ##\delta Q## to a system and observing the resulting change in internal energy : $$\delta U =...

Homework Statement A unknown nuclide emits four alpha particles with energies 8.54, 7.04, 6.38, and 5.10 MeV a) what are the nuclear energy levels of this nuclide b) What are the possible gamma ray energies that should be observed[/B]Homework EquationsThe Attempt at a Solution I was trying...

Homework Statement In the earliest circular planetary model of the atom the electron and proton orbited a common centre. The electrostatic forces alone provided the force field. However an accelerating charged body will send out electromagnetic waves and the orbiting charges would consequently...

Derivation of energy levels in a quantum harmonic oscillator, ##E=(n+1/2) \hbar\omega##, is long, but the result is very short. At least in comparision with infinite quantum box, this result is simple. I suspect that it can be derived avoiding Hermite polynomials, eigenvalues, etc. I understand...

I have previously learned about the energy level calculation of some diatomic molecules, such as N2 and CO. Now I need to calculate the spherical top symmetric molecules like CH4. But I cannot find the force constants for it either, can anyone give me some suggestions about this?

Hello! Let E_1, E_2, \ldots, E_n be n allowed energy levels for a system of electrons. This system can be described by the Fermi-Dirac distribution f(E). Each of those levels can be occupied by two electrons if they have opposite spins. Suppose that E_1, E_2, \ldots, E_n are such that...

Why is is true that for a given system, if I fix the volume and increase the temperature, you'd expect the occupancy of the energy levels to change, but not the levels themselves? Can I think of this in terms of the fact that the boundary conditions for the solution of the TISE are fixed, such...

So if energy levels, or eV of electrons, do not change with molecular bonding, how are electrons influencing each other.? In glass, when individual atoms of silicon, sodium, and calcium come together, to form glass, the molecular bonding does not change the energy levels of the electrons for...

So in glass, transparent liquids, and plastics is the eV for the electron known to science. The eV levels for electrons in gases are known like in hydrogen, and helium, but are they known for glass, and transparent liquids, and plastics. Or is it just too discernable to get. I am grateful for...

How can a electrons energy levels increase, and decrease in eV As atoms come together to form molecules the energy levels of electrons change in eV, but are there other ways a electrons eV can change. Can heating a material change the electrons eV level, when visible light hits the electrons...

So I'm trying to figure out how we got the allowed vibrational energy levels for a diatomic molecule by approximating it with simple harmonic motion. I do know how to use the uncertainty principle to get the zero-point energy: We know that the potential function is ##V(x) = \frac{1}{2}mx^2##...

how does the quantum number n in the wavefunction equation for a particle in a 1D box lead to increasingly well-separated energy levels? I know that the separation of energy between the levels is given by ΔE = (2n+1)h^2 / 8mL^2 which means that the higher the n, the greater the energy...

i am trying to understand the magnetocaloric effect from another point of view (besides thermodynamics ) , i know that under the influence of an external field , a zeeman splitting happens , and the electrons will have different levels of energy , those with + 1/2 spin will have a higher energy...

Okay so I just had another (silly) doubt Consider a hydrogen atom (1 proton in the nucleus and 1 1s electron) We know that the total energy of the hydrogen atom in its ground state is -13.6 eV And let's say in order to excite the electron to jump to n=2 the total energy should be -13.6/4=-3.4eV...

Homework Statement I'm reading some text on solid-state lasers and a passage that struck me was this: "The low-lying energy levels of the ion are determined by the forces acting on and between the electrons in unfilled shells. (The electrons in unfilled shells can be regarded as inert.)" If...

Hello, I wonder how the speed of interaction affects the energy levels in atoms. We know that electrons in atom are attracted to the protons in the nucleus through the electromagnetic force. Photon, the force carrier for the electromagnetic force, moves in empty space with the speed c (the...

I don't know where I'm going wrong with this problem - I was so sure I had it right but the online grader tells me otherwise :oldfrown: Homework Statement An electron in a one-dimensional box has ground-state energy 2.60 eV. What is the wavelength of the photon absorbed when the electron...

If there was a bond in the 2p vs 3p subshell, which would be stronger? Taking into consideration that they are in the same group Thanks

Although I have not been thinking very much about actual physics for while now I suddenly got the urge to read a little bit about it and I decided to start by checking out the birth of quantum mechanics again. In the book quantum theory by Bohm in chapter 1 the ultra-violet catastrophe and its...

Homework Statement *This is not my whole problem, I am only stuck on how to interpret one part of the question. Put simply, I want to find the expression for the density of energy levels in a given energy band per unit volume (in some crystal structure). Say I have an infinitesimal interval of...

Homework Statement Find the energy levels of a spin ##s=\frac{3}{2}## particle whose Hamiltonian is given by: ##\hat{H}=\frac{a_1}{\hbar^2}(\hat{S}^2-\hat{S}_x^2-\hat{S}_y^2)-\frac{a_2}{\hbar}\hat{S}_z## where ##a_1## and ##a_2## are constants. Homework Equations In the ##\hat{S}_z## basis...

Dear all, I was wondering about the problem of calculating the probability that an electron will tunnel through a certain barrier (let's assume it is a constant value). Problem is that the initial and final energies of the electron are fixed and possesses a certain broadening (for example...

Say we have a Quantum Dot with $$n=10^{26}m^{-3}$$ and radius $$R = 3nm$$ then this will give us of the order of 13 electrons. My question is how do you relate the number of electrons to the quantum numbers n and l in order to use the spherical Bessel function values? In class for 13 electrons...

Homework Statement Draw an energy level diagram for hydrogen (use the vertical direction for energy and separate the states horizontally by angular momentum l) Homework Equations I've got some fundamental misunderstandings with this one. I thought the energy levels of hydrogen were given by...

Homework Statement A 0.39 kg mass falls from a height of 2.9 m. If all of the energy of this mass could be converted to visible light of wavelength 5.5 × 10^−7 m, how many photons would be produced? The acceleration of gravity is 9.8 m/s^2 . Planck’s constant is 6.63 × 10^−34 J · s, and the...

Homework Statement A 0.39 kg mass falls from a height of 2.9 m. If all of the energy of this mass could be converted to visible light of wavelength 5.5 × 10^−7 m, how many photons would be produced? The acceleration of gravity is 9.8 m/s^2 . Planck’s constant is 6.63 × 10^−34 J · s, and the...

Dear Everyone, If we have a set of diatomic molecules consisting of a common element (F atom) and the other atoms belong to the same group; which are: BeF, MgF, CaF, SrF, and BaF. We want to study the electronic structure of these molecules by comparing their molecular electronic states. We...

See photo attachment! (question 1(b) and see answer on mark scheme underneath) How can three photons be emitted? Either the electron drops down from 3 to 1 and skips 2 emitting one big 12.1 eV photon OR it falls down in step emitting two photons 1.9eV and 10.2eV. How can it emit more energy...

Hi PFs whith atoms in the ground level |g> we can prepare them in the first excited energy level |e> by giving them the transition energy with a laser. if one photon is absorbed it will be in |e>. I read that to prepare a |e> + |g> state i can use a ##\pi/2## pulse with this same laser. What is...

As the atoms of a material are brought closer together to form the crystal lattice structure, there is an interaction between atoms, which will result in the electrons of a particular shell of an atom having slightly different energy levels from electrons in the same orbit of an adjoining atom...

Hello, I was trying to solve a problem in my course book, and I noticed I don't really understand energy levels completely. My ignorance covers more than one specific problem, so I figured I'd ask a general question, rather than post the problem. The Rydberg formula: ##...

Why do electrons further away from the nucleus have more energy? When my book mentions energy in different orbitals, is it talking about potential energy? If it is, I'm confused because potential energy is inversely related to distance, so if distance increases, the potential energy decreases.

Homework Statement I must find the average number of energy levels of quantum harmonic oscillator at temperature T, and the answer is given as I must use Boltzmann distribution and the sum of geometric progression. For finding the average value I must use the equation <F>=trace(F*rho)...

I noticed something about the normalized wave function solution to the particle in an infinite square well (which has the boundary conditions v(x)= ∞ at x = 0 and x = L , and v(x) = 0 in between those two). The solution is: Ψ(x) = (2/L)½ * sin(πnx/L) where n is an integer that signifies...

Neon is the lasing element in He-Ne laser. The lasing transition(632.8nm) is from 3s to 2p. In the energy level diagram there is one 1.15μm transition from 2s to 2p. But we studied that 2s orbital have lower energy than 2p then how it is possible, in the energy diagram, 2s level have higher...

Homework Statement Silicon has the configuration [Mg] ##3p^2##. Explain why there are more L, S, J levels for the ##3p4p## configuration than in the ##3p^2## configuration. Homework EquationsThe Attempt at a Solution My thought is because in the ##3p^2## subshell you have less variations of...

Homework Statement Hi, I've been unable to find a relevant thread for a question that I've been stuck on for a couple of days now. Here it is; One of the electromagnetic emission lines for a hydrogen atom has wavelength 389nm. Assiming that this is a line from one of the Lyman (nf =1 )...

when considering the quantum harmonic oscillator, you get that the wave function takes the form psi=ae^{-\frac{m\omega}{2\hbar}x^2} I have been trying to integrate \psi ^2 to find the constant a so that the wave function is normalised, and I know the trick with converting to polar coordinates...

Hello! I am reading about the creation and annihilation operators and I don't get how you find the creation operator from the annihilation one. The creation one is \hat{a}=\sqrt{\frac{m \omega}{2 \hbar}}\left( \hat{x}+\frac{i \hat{p}}{m \omega}\right) and the annihilation operator is...

Consider a potential well in 1 dimension defined by $$ V(x)= \begin{cases} +\infty &\text{if}& x<0 \text{ and } x>L\\ 0 &\text{if} &0\leq x\leq L \end{cases} $$ The probability to find the particle at any particular point x is zero. $$P(\{x\}) = \int_S \rho(x)\mathrm{d}x=0 ;\forall\; x \in...

if you take a hydrogen atom and strip off the electron so that you are left with a proton. does the proton have energy levels around it? can a solitary proton still be regarded as an atom (H+)