Hydrogen atom Definition and 410 Threads

Homework Statement While playing around with basic QM, I tried using the hamilton operator to find the kinetic energy of a hydrogen atom in its ground state. I assume the wave function ##\psi_1## is known. However, I of course ran into problems... 1) in my solution attempt below, I end up with...

Homework Statement Electron in Hydrogen atom can be described with wavefunction ##\psi =\frac{1}{2}(\psi _1+\psi _2+\psi _3+\psi _4)## where ##\psi _1=\psi _{200}##, ##\psi _2=\frac{1}{\sqrt{2}}(\psi _{211}+\psi _{21-1})##, ##\psi _3=\frac{i}{\sqrt{2}}(\psi _{211}-\psi _{21-1})## and ##\psi...

Homework Statement I am given a linear combination of wave function of HYDROGEN ATOM Ψ=1/2(Ψ200 +Ψ310+Ψ311+Ψ31-1), where the subscripts are n, l, m respectively. I was asked to find all the possible outcomes when measuring Lx and their corresponding probabilities. Homework Equations...

Homework Statement Hey dudes So here's the question: Consider the first excited Hydrogen atom eigenstate eigenstate \psi_{2,1,1}=R_{2,1}(r)Y_{11}(\theta, \phi) with Y_{11}≈e^{i\phi}sin(\theta). You may assume that Y_{11} is correctly normalized. (a)Show that \psi_{2,1,1} is orthogonal...

Homework Statement Hey guys, so here's the question: The energy eigenstates of the hydrogen atom \psi_{n,l,m} are orthonormal and labeled by three quantum numbers: the principle quantum number n and the orbital angular momentum eigenvalues l and m. Consider the state of a hydrogen atom at t=0...

Homework Statement Evaluate the matrix element <U210|z|U100> where by |Unlm> we mean the hydrogen atom orbital with it's quantum numbers. Homework Equations The Attempt at a Solution So where I'm getting stuck is on the integral, because the "U" portion of the wave function is...

Homework Statement A hydrogen atom is in 2p state, how many different energy levels are there if a magnetic field of 0.10 T is applied to it, and what are their energies? Make sure spin is included. Homework Equations U = -gmsμzB g is the Lande-g factor, which is about -2 for...

Homework Statement What is the probability that an electron in the ground state of hydrogen is within one Bohr radius of the nucleus? Homework Equations P_{nl}(r) = r^{2}|R_{nl}(r)|^{2} The Attempt at a Solution Since it's an electron in the ground state of a hydrogen atom, that...

According to Einstein's equation, E=mc^2, I calculated the energy from one hydrogen atom to be roughly 5.01*10^-15 Newtons. I am unsure as to if this is correct. Please help me.

Homework Statement Hi, my question is regardng a Coulomb model of an H atom specified with Hamiltonian operator, Hhat, by spherical coordinates of energy eigenfunction ψ2,1,-1 (r,θ, ∅) =(1/ 64∏a02)1/2 r/a0 e-r/2a0 sinθ e-iθ Principal quantum numer n = 2 orbital an mom l = 1 magnetic...

I have a couple of questions about selection rules for the hydrogen atom. When we talk about these rules in an undergraduate context we are usually assuming LS coupling where we ignore spin orbit coupling so orbital and spin angular momentum are essentially independent. Is that correct...

Consider the following. You have an electron of negative charge orbiting a proton of positive charge at some distance R (i.e. a classical hydrogen atom). I understand the hydrogen atom is unstable under classical physics because the accelerating electron loses its kinetic energy as...

Homework Statement • Consider a hydrogen atom in its ground level, placed in a magnetic field of 0.7 T along the z axis. (a) What is the energy difference between the spin-up and spin-down states? (b) An experimenter wants to excite the atom from the lower to the upper state by sending in...

A stationary hydrogen atom with a mass of 1.67 x10^-27 kg absorbs a photon of light with an energy of 10.2eV.What is the velocity of the hydrogen atom after absorbing the photon? This is my question: Is it true that the atom has no speed since all the energy is completely absorbed at the...

Typically (in popular literature) the process of photon emission by an excited atom is considered as an instant event. But actually it is quite likely that it is a continuous process. Such processes are usually described by evolutionary differential equations (ODEs or PDEs). Assume that we...

I am wondering about acceleration in quantum mechanics. Let's consider spherically symmetric potential V(r). From the Heisenberg equation of motion, one finds the time derivative of the momentum operator \dot{\hat{p}}=\frac{i}{\hbar}\left[\hat{H},\hat{p}\right] = -\nabla V, from which we can...

Homework Statement Hydrogen is in n=2, l=1, and m=0. Wave function is ψ(r,θ,∅)=(1/4(√2pi)ab3/2)(r/ab)(e-r/2ab)(cos(θ) Find <r> for this state. Homework Equations P(r) = 4pir2|R(r)|2 <r> is equal to the integral from 0 to ∞ of P(r)dr The Attempt at a Solution I understand...

Do hydrogen atoms have inner and outer electron shells? I saw a diagram somewhere that showed a carbon atom with an inner and outer shell, is this proven? Are these shells magnetic or something else? Do you consider the outside of these shells as the diameter of the atom?

When you solving Sroedinger eq for hydrogen atom you get energy values ##E_n\approx \frac{1}{n^2}##. Why for some value of this energy electron don't leave atom?

Homework Statement The ground state of the hydrogen atom has the wavefunction: \psi (r) = \frac{1}{\sqrt{\pi}} (\frac{1}{a_{0}})^{\frac{3}{2}} e^{-r/a_{0}}, where a_{0} = 0.53Å a) Calculate the probability that an electron will be found inside the nucleus of the hydrogen atom, which is...

Homework Statement Individual hydrogen atoms have been prepared in the energy state n = 2. However, nothing is known about the remaining quantum numbers. Fine structure and all corrections can be ignored. What is the micro-canonical statistical operator. Homework Equations \hat{\rho_{mc}} =...

When solving the three dimensional Schrödinger equation, we obtain a probability distribution on θ. But it seems like the procudure produces a particular direction the z-axis. While the Coulomb field is spherical symmetric, it shouldn't exist such a preferred direction. I'm puzzled.

What potential would one use when evaluating the Dirac equation of the hydrogen atom? Would it simply be in the form used when examining the hydrogen atom-Schrodinger equation or does it need modification?

I'm studying the Bohr's hydrogen atom and my teacher gave us a challenge question. When I was working in the problem I've got a couple of other questions that I don't know the answer. The initial problem was the following: Today we know the electrons are not the only particles moving inside...

I have a fairly straightforward question: how does one formulate the problem of hydrogen atom with quantum field theoretical treatment? I understand that one can just take Uehling potential and find approximately the bound states' energies and wave functions, but it would not make electron...

Homework Statement Hi guys the question is "Write down the time independent Schrödinger equation for the hydrogen atom, and show that the wave function Ψ(r,θ ,φ ) = Ae(−r / aB) is a solution. (A is a normalization constant and aB is the Bohr radius.) What is the energy of the state with this...

When I write down the Hamiltonian for the hydrogen atom why do we not include a radiation term or a radiation reaction term? If I had an electron moving in a B field it seems like I would need to have these terms included.

A hydrogen atom is in its ground state and is subject to an external electric field of E = ε(\hat{x}+\hat{y}+2\hat{z})e-t/\tau I'm confused as to how to compute the matrix elements of the perturbed hamiltonian since this is not in the z direction. Would I have to do something like this...

Homework Statement What are the orbital angular momentum possible values for an electron in a hydrogen atom with a principal quantum number n = 3? Homework Equations L = \sqrt{l(l+1)}\hbar The Attempt at a Solution Possible values for l are 0, 1, 2. So, substituting these in...

Homework Statement Whenever a photon is emitted by hydrogen atom in the Balmer series, it is followed by a photon in Lyman series . What wavelength does this latter photon correspond to ? Homework Equations Balmer series corresponds to the wavelengths in the visible spectrum and Lyman...

Homework Statement What is the energy of H atom in the first excited state if the potential energy in the ground state is taken to be 0 ? Homework Equations Usually the energy of H atom in the ground state is -13.6eV and in the 1st excited state is -10.2eV E(n) = πme2/8ε2h2 Bohr's...

Homework Statement A Hydrogen atom is in a state with n=2? Homework Equations r=an^2 a=.0529 nm The Attempt at a Solution I am confused by my book it says that the radius of a stationary state is r=.0529*2^2=.2116 but I disagree isn't the stationary state n=1 which would mean the...

Homework Statement A hydrogen atom in an excited state absorbs a photon of wavelength 434 nm. What were the initial and final states of the hydrogen atom? Homework Equations 1/λ=1/91.127 * (1/nf2-1/ni2) The Attempt at a Solution Tried to use the equation, but keeping the initial...

I am studying for my exam and I have run into this problem. The problem is given here http://faculty.mint.ua.edu/~pleclair/PH253/Homework/Spring_2010/HW6-7_atoms_12Mar10/HW6-7_atoms_12Mar10_SOLN.pdf"],[/PLAIN] it is #9. I don't understand why -e ≠ ∫ρdV from 0 to the bohr radius, a0. If all...

A sole hydrogen atom in a vacuum (negligible gravity). The hydrogen atom has the lowest possible kinetic energy allowed by QM. Given that casimir effects apply... Will the hydrogen atom remain at it's initial lowest kinetic energy state indefinitely or is it possible for it's energy state to...

Hi,Everyone! I have a question! We often say hydrogen atom spectrum. But in nature ,it exists in the form of molecular hydrogen. today, I read something about hydrogen atom spectrum experiment. In the experiment ,we use hydrogen lamp. The Hydrogen lamp is a long glass tube filled with Hydrogen...

is it pauli or schrodinger? is there any original reference?

All I need to evaluate the normalization coefficient. I need a step by step guide. It will be a great help if someone please tell me where can i get the solution (with intermediate steps). I think the solution can be done using the orthogonal properties of associated Laguerre polynomial. I need...

"Prove that the Bohr hydrogen atom approaches classical conditions when [. . .]" Homework Statement The problem and its solution are attached as ProblemSolution.jpg. Homework Equations E_k = chR/(n_k)^2 E_l = chR/(n_l)^2 ΔE = hc/λ hc/λ = chR[1/(n_k)^2 – 1/(n_l)^2] 1/ λ = R[1/(n_k)^2 –...

What exactly is it that makes the energy/mass of a hydrogen atom be lower than that of the electron and proton separately? I am aware that this process is what causes stars to emit light, during nuclear fusion deuterium has a smaller mass than a proton and a neutron so its extra mass/energy is...

We know this tiny splitting in degenerate levels in Hydrogen spectrum due to magnetic interactions between spins of electron and proton. but is that true the proton spin is independent of energy in this (hyperfine) splitting? I want to understand the physics of this splitting and how the spin...

why is hydrogen the only element in the periodic table that lacks a neutron?

The term (E-V) which stands for kinetic energy is used in Schrodinger equation.Kinetic energy of electron needs motion and fixed path which leads to the conclusion that electron is moving around the proton in orbits and is not spread out because derivation of Schrodinger equation is based on...

if delocalization of electron in hydrogen atom means that it is spread out upto infinity it means that infinite time is required for the electron to be localized when hydrogen atom is ionized.Is it so?

Homework Statement Find the constant A such that the equation \psi(r,\theta,\varphi)=\sqrt{6\pi}A\sqrt{r}e^{-r/a} Wich describes one electron in a hydrogenatom, is normalized The Attempt at a Solution I figured this equation is seperable in the form...

I'm here got a small question, what is the different between L2 and L for the hydrogen atom. Do L2 means total angular momentum and L means angular momentum?:confused: Given that L2=l(l+1)ℏ2 and L=(√l(l+1))ℏ THX :smile:

I just did exercise 1.22 in Modern Quantum Chemistry by Szabo and Ostlund. This is a practice problem about linear variational method. ---------------------------------------------------------------------------------------- Question: The Schrodinger equation(in atomic units) for a hydrogen atom...

The Schrodinger equation solved for the hydrogen atom gave good agreement with spectral lines, except for line doublets. To account for these electron spin theory was grafted onto the theory, despite the problem of electron being a point particle. In 1928 Dirac gives his different answer...

What is the uncertainty speed of a hydrogen atom inside a virus? Even though the vaue of uncertainty in position is not given. Any help on this would be greatly appreciated. Thanks!

Homework Statement The problem (4.13 (b) in Grifitths) asks to find <x^2> of the ground state of hydrogen atom. It asks to do so without new integration. Supposedly, there is some kind of symmetry and one can use the results from part (a) of the problem. Part (a) is finding <r> and <r^2> for...