Hydrogen atom Definition and 410 Threads

Homework Statement Given the following recursion formula: b_{j} = 2 \frac{kj - a}{j(j+1)-l(l+1)} \cdot b_{j-1} (where a, k and l are constants) how can b_{j = l} \neq 0 if b_{j - 1} = 0. Homework Equations The Attempt at a Solution This is a part question and I really can't see why. if...

Hi all How does one calculate the recoil velocity of a hydrogen atom when the electron in it jumps from a higher orbit to a lower orbit (say from 3rd to 1st) ?

Assume the universe consists of a single photon, a single atom of hydrogen and a spherical detector (like an encompassing shell) with a semi-infinite radius. The photon gets "absorbed" by the hydrogen atom. Moments after the photon is emitted. My question is the following: from the time...

I almost have the answer, I'm sure there's just a minor flaw in my reasoning. Here it goes: We're given that the angular momentum of the atom is integer multiples of h-bar (n\hbar) (integer depending on the orbit). Now the centripetal force is given by F = \frac{mv^2}{r} = \frac{p^2}{mr} =...

If a a 1s hydrogen atom is placed in a B field, how many energy states will it split into?

Hi everyone! So we're learning about the Hydrogen atom in QM and I'm having trouble reconciling something in my head. We're looking at potentials that are only radius dependent, like the Coulomb potential. Now, I know the math. I see that we assume the wave function can be separated into the...

Homework Statement In Bohr’s hydrogen atom, the frequency of radiation for transitions between adjacent orbits is νBohr = (En+1−En)/h. Classically, a charged particle moving in a circular orbit radiates at the frequency of the motion, νorbit = v/2πr. Find the ratio νBohr/νorbit for the...

When (what year and by whom?) was it discovered that the hydrogen potential is V=-1/r ? I imagine this was deduced from experimental data... amirite? Quite urgent... From wiki it looks like it was found in teh 1920's but I'm not certain so I just want to check. Thanks in advance

when proton and electron combine to form hydrogen atom(ground state) what is the source of radiation emitted

Homework Statement The average function of the H-atom in its ground state is ψ(\vec{r})=(1/(πa03)1/2exp(-r/a0) a0: Bohr radius a.What is the probability i. P(\vec{r})d3\vec{r} that the electron will be found in the volume d3\vec{r} around \vec{r}? ii. Pdr that the electron will be found...

Homework Statement Determine for the hydrogen atom states 1s and 2p the expectation value of the radius r and the associated mean square error Δr. Homework Equations Wave Functions for 1s and 2p from Demtroeder's Experimental Physics Volume 3 (it says "The normalized complete...

As I know from the laws of chemistry,to form H_2 the H atoms must have opposite spin. What if they have the same spin? I mean, can an H atom rotate to swap his spin (i'm not expert of the dynamics of spin), or there is no way to couple them? In the case I have a gas of H with all of them...

Homework Statement The level n=3 for atoms with 1 electron have the states 3s_{1/2}, 3p_{1/2}, 3p_{3/2}, 3d_{3/2}, 3d_{5/2}. If we ignore the spin-orbit coupling these states are degenerated. Calculate the degeneration due to the the spin-orbit coupling for the levels 3p and 3d for the...

Homework Statement In a classical model of the hydrogen atom, the electron moves around the proton in a circular orbit of radius 0.053 nm. What is the electron's orbital frequency? What is the effective current of the electron? Homework Equations Freq * Wavelength = Speed of...

Calculate the expectation value of the potential energy for an electron in a 1s orbital for a hydrogen atom Ive determined the potential energy operator to be V=-e2/4∏ε0r and a wave function of ψ= (1/4∏)1/2 therefore i get <V> = ∫∫∫ψ*Vψr2sin∅drd∅dphi integrals from 0 to r...

Homework Statement The DE y''+\frac{2}{x}y'+ \left [ K+\frac{2}{x} - \frac{l(l+1)}{x^2} \right ]y=0, 0<x< + \infty. appears when working on the hydrogen atom. Find all the values of K (the eigenvalues) that generates solutions of the form \phi (x) such that \phi (x) remains finite when x...

Energy level of hydrogen atom -- with the electron replaced by a positron The energy level of a hydrogen atom is given by (without fine structure consideration) Eh = -13.6 eV / n^2 Suppose -- if the electron is replaced by a positron, what would happen to this energy level? The resulting...

Homework Statement An electron in a hydrogen atom is described by the wavefunction: psi(r) is proportional to (psi(subscript 100)+2psi(subscript 210)-3psi(subscript 32 -1) -4psi(subscript411)) where psi(nlm(subscript l)) are the eigenfunctions of the hydrogen atom with n, l...

Homework Statement 1)Determine the radius of the allowed orbits. Calculate the first orbit of Bohr's model for the hydrogen atom. 2)Show that the energy is quantized. Calculate the energy of an electron on the first orbit (fundamental state of hydrogen atom)Homework Equations L=n \hbar...

I'm trying to plot the radial probability function for a hydrogen atom. I have the function itself (Psi2*4*pi*r2) my problem is that when I plot the function with angstroms on the x-axis, the y-values are larger than they should be (they look about right if I divide them by the bohr radius in...

Hello, I am currently reading about electromagnetic fields: In one of the examples in the textbook we calculate the electric field of a hydrogen proton. We then compute the electric force acting on the orbiting electron to be 8.2 \times 10^{-8} N So I thought I could get the...

I am attempting to find the probability, after time t, of a hydrogen atom in a magnetic field \vec{\mathbf{B}}=B_0\hat{\mathbf{z}} to go from \left|n,l,s,j,m_j\right\rangle \longrightarrow \left|n',l',s,j',m_j'\right\rangle where j=l+\frac{1}{2} and j'=l'+\frac{1}{2} or...

Is there any derivation of the bohr model for hydrogen using Ehrenfest theorem. References are appreciated.

I do not understand if you accelerate a hydrogen atom to 90% the speed of light its mass is greatly increased. Are the forces that hold it together increased? If not how is it different, will it fall apart? If the forces are increased in relationship to the mass of the atom the energy...

Homework Statement Use [H_{0},r_{j}]=\frac{i\hbar}{\mu}p_{j} for the Hydrogen atom (where the j's denote the jth components in Cartesian coordinates) to prove that <n_{f},l_{f},m_{l,f}|p_{j}|n_{i},l_{i},m_{l,i}>=-i\mu\omega<n_{f},l_{f},m_{l,f}|r_{j}|n_{i},l_{i},m_{l,i}> Homework...

Homework Statement So I've been racking my brain around the hydrogen mean values. \left\langle \frac{1}{r}\right\rangle=\frac{1}{a_0n^2}, that I can solve with the recurrence relation in Schaum: \left\langle r^k\right\rangle=\int_0^\infty r^{k+2}|R_{nl}(r)|^2dr by simply putting in...

Most common isotopes of He has 2 neutrons, Li has 3 neutrons and so on right, until Z increases to higher numbers and we get to elements like iron, where the nucleus doesn't have equal numbers of protons and neutrons anymore. But why isn't the number of protons and neutrons equal in the most...

I noticed many PF threads mention ground state of Hydrogen atom. At the same time it is two body problem considered to be solved by separation of variables. It is true, of course, that we can find basis wave functions (solutions of Shroedinger equation). But why does anybody think, that...

Just a quick question regarding the solution of the hydrogen atom: is it possible to solve the hydrogen atom problem via creation and annihilation operators as is the case with the harmonic oscillator? Any help here greatly appreciated! Crawf.

hi does anybody of you know if there is an equation that describes an atom in a gravitational field of a star or something like that (general relativity or Newton)or do you know some results that could tell me something about the magnitude of this energy corrections? do you know a method...

A hydrogen atom placed in an electrical field results in a changed energy level and a changed eigenfunction, compared to the free atom. To examine this effect, we choose a homogenous electrical field of the force F, whose field lines run along parallel to the z-axis. The Schrödinger equation is...

Hello! I'm preparing for my quantum mechanics test. In the solutions of an old test I find this conversion, that I don't understand. \Psi = Nze^{-r/2a_0} = Nre^{-r/2a_0}cos\Theta N is the normalization constant, which is to be calculated. I would have guessed that z is the atomic...

I have a question about the stability of positronium. Positronium consists of an electron and a positron whereas hydrogen consists of an electron and a proton. The energy levels of positronium, ignoring fine structure, are -6.8eV/n2 whereas those for hydrogen are -13.6eV/n2. My question...

Hi, I was wondering if the bound solutions to the radial part of the hydrogen atom form a complete set for the functions in L^2(0,\infty). I know that the laguerre polynomials are complete and that they only differ from the radial solutions by factors of x^l * exp, so I thought that they would...

Hey, probably a stupid question but I can't seem to find an answer anywhere. Is a hydrogen free radical just a single hydrogen atom? A hydrogen atom has an unpaired electron bound right? Thanks in advance

Homework Statement An electron of know KE collides with a hydrogen atom in its ground state. With what possible KE may it rebound? KE = 11.5 eV 2. The attempt at a solution I assumed that the electron may either hit an orbiting electron and excite him (maximum layer is n = 2, change in KE...

hi i asked myself, is it correct to use the ordinary partition function and cut it off at some value to describe the atom at some finite temperature? or is there a better way to do this calculation? and if i evaluate the partition function for let me say n=2. does this mean, that the...

I haven't posted any of my working for this as I only want to check my answer. Q. For a hydrogen atom with n=2, l=1, m=0 calculate <r^2> My answer = 0.75 * a^2 where a is the bhor radius. Am I right?

Homework Statement I need to calculate the probability distribution of 1s and 2p state of hydrogen atom in momentum and in coordinate representations. I have calculated the wave function in coordinate representation, and the dilemma is, do I simply do the Fourier transform for given wave...

Homework Statement Define the quantum numbers required to specify the state of an electron in hydrogen. The spatial part of the wave-function describing a particular hydrogen atom has no angular dependence. Give the values of all the angular momentum quantum numbers for the electron...

Hydrogen Atom ---> Uncertainty Principle Hey guys, I'm having some trouble with this one. [PLAIN]http://img849.imageshack.us/img849/2039/physhw.jpg How do I get started?

Consider a hydrogen atom whose wave function is at t=0 is the following superposition of energy eigenfunctions nlm(r) (r, t=0) = *[2100(r) -3200(r) +322(r) What is the probability of finding the system in the ground state (100? in the state (200)? in the state (322)? In another energy...

Consider a hydrogen atom whose wave function is at t=0 is the following superposition of energy eigenfunctions \psinlm(r) \Psi(r, t=0) = \frac{1}{\sqrt{14}} *[2\psi100(r) -3\psi200(r) +\psi322(r) What is the probability of finding the system in the ground state (100? in the state (200)? in...

1. Consider Bohr Hydrogen atom with counter-clockwise electron orbit in the xy plane with intial position r(0)=-a0y. The angular frequency of the orbit is w. Derive an expression for the position of electron at a later time t, r(t) in terms of a0 , w, t, x, and y. Homework Equations...

I've heard that the hydrogen atom that we originally learn about in QM that deals with the Coulomb force is an incomplete description. I'm having trouble understanding all of these effects. When describing the electron energy of the real Hydrogen atom, how do things like the zeeman effect...

Hi everyone, How can I solve hydrogen atom with discrete nonlinear schrödinger equation? Could you help me with the mathematics of that, please?

Hi. I'm a 3rd year undergraduate studying Applied Physics and I'm having some trouble with a problem concerning the Hydrogen Atom. This is my first post so please forgive the sloppy equations. Not really used to writing this stuff out without an equation editor handy! Anyway, the...

Hi, I'm trying to figure out the solution for the ground state of the hydrogen-atom, however it is not going well. As far as i know, you can supress the angular dependence, because the states of hydrogen (or at least some of them) are spherically harmonic. This way the schr. equation just...

In the position representation, its true that we can use operators to represent the coulombic interaction between the proton and electron of a Hydrogen atom. I've never actually given any thought as to what the elements of such an operator would be (in matrix form of course). I know these...

Homework Statement An initial state is given: {\lvert {\psi(0)} \rangle} = \frac{1}{{\sqrt{3}}} \left( {\lvert {100} \rangle} + {\lvert {210} \rangle} + {\lvert {211} \rangle}\right) An L_z measurement is performed with outcome 0 at time t_0. What is the appropriate form for the ket...