Hydrogen atom Definition and 397 Threads

Suppose a single hydrogen atom is in mixed state. Ψ=(1/√2) Ψ_100+(1/√2) Ψ_200 Then energy will be E=(1/2)*13.6+(1/2)*(3.4)=8.5 eV. But there is no spectral line at 8.5 eV.

For hydrogen atom ground state we know φ=π-1/2a-3/2e-r/1 I want to know the complex conjugate of φ* ?

Consider the Dirac equation for bounded electron in hydrogen atom. I am trying to get a clear physical explanation for all mathematical terms that appear in the Hamiltonian and energy spectrum. Kinetic and Coulombic potential and rest energies are the first terms and easy to identify. Then we...

Question: In the Bohr model of the hydrogen atom, the speed of the electron is approximately 2.18 × 106 m/s. Find the central force acting on the electron as it revolves in a circular orbit of radius 5.02 × 10−11 m. Answer in units of N. Comment on Attempt: Ok I tried using the centripetal...

Homework Statement In general, how would one calculate total probability/ in Hydrogen atom in two different states (n values)? Homework Equations P(r) = dP/dr = r^2R(r)^2? The Attempt at a Solution ?

Homework Statement Show that in terms of the dimensionless variable ##\xi## the radial equation becomes ##\frac{\mathrm{d}^{2} u}{\mathrm{d} \xi^{2}}=(\frac{l(l+1)}{\xi^{2}}-\frac{2}{\xi}-K)u## Homework Equations ##u(r)\equiv rR(r)## ##\xi \equiv \sqrt{2\mu U_{0}}\frac{r}{\hbar}##...

Homework Statement "Suppose that a hydrogen atom, initially in its ground state, is placed in an oscillating electric field ##\mathcal{E}_0 \cos(\omega t) \mathbf{\hat{z}}##, with ##\hbar \omega \gg -13.6\text{eV}##. Calculate the rate of transitions to the continuum." Homework Equations ##R =...

Suppose the hydrogen atom consists of a positive point charge (+e), located in the center of the atom, which is surrounded by a negative charge (-e), distributed in the space around it. The space distribution of the negative charge changes according to the law p=Ce^(−2r/R), where C is a...

Homework Statement We have a crude model for the polarization of a hydrogen atom, by approximating its 1s orbital with a uniformly charged ball of radius a. What is the (negative) charge density of the electron cloud? What is the electric field inside the cloud, at the point with radius vector...

Hi guys, I consider the qm-derivation of the electronic states of hydrogen. There are two different derivations (I consider only the coulomb-force): 1) the proton is very heavy, so one can neglect the movement 2) the proton moves a little bit, so one uses the relative mass ##\mu## The...

The answer according to my booklet is 1.6734×10-24 (g), but I don't understand how we got this answer. proton: 1.6725×10-24 neutron: 1.6748×10-24 electron: 0.0009×10-24 To get the mass, I added protons with neutrons, but I got 3.3473×10-24. What am I doing wrong?

Homework Statement [/B] Consider a hydrogen atom which, in t = 0, is in the state given by \psi(\mathbf{r},t>0)=\frac{A}{4\pi}R_{10}(r)+\frac{cos\alpha}{4\pi}\left(\frac{z-\sqrt{2}x}{r}\right)R_{21}(r) Expand ψ in terms of the {Φnlm} basis of normalized eigenfunctions...

I am interested in what the recoil velocity of an initially stationary hydrogen atom in free space would be when it emits a Lyman alpha photon. I tried to do the calc and got about 3 metres per second which seems rather high.

U(x,y,z,t)*ψ(x,y,z,t)-(ħ/(2*m))*(d2ψ(x,y,z,t)/dx2+d2ψ(x,y,z,t)/dy2+d2ψ(x,y,z,t)/dz2)=ħ*i*dψ(x,y,z,t)/dt qproton=-qe Schrödinger equation for electron in hydrogen atom (if we consider proton as point charge which is moving at a constant speed vproton→=(vp;x;vp;y;vp;z).) is...

What's the mass difference between a hydrogen atom and it's constituent particles when they are free, I'm talking about the proton and the electron, not the quarks that make up the proton.

Hey I was reading through a text and came across: I can understand the second statement from the Pauli matrices... However I think that I don't understand the 1st statement as it is... why would the diagonal elements of an odd-operator be zero if parity is definite?

Does the energy of the electron in a random hydrogen atom is in superposition of all eigenvalues(some value upon measurement) or you will find it most likely in the ground state. Additional clarification: From my reading the textbooks said the electron energy is in superposition, yet the...

Given a 2 state hydrogen atom in a superimposed state, how does one measure it for either of its two states?

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...

Just look at the first point.It says the given compound has four types of hydrogen atom.How?I can only see three types of hydrogen atom primary,secondary and tertiary which is the fourth type?Please give me a hint.

What happens if a hydrogen molecule is stripped of an electron? Will it become 2H+ or will it become H and H+?

This question is in regards to the degeneracy of states for an Argon atom with just one missing electron. For hydrogen the problem of finding the partition function depends on finding the the ionized state of hydrogen divided by the non-ionized state... (please see Saha equation ->...

I've been following the EdX course on Quantum Computing by Prof. Vazirani and I don't understand how one physically can create a superimposed state of the ground and 1st excited state of an hydrogen atom. He mentions "the use of light," but doesn't explain the frequency of the light, nor the...

I was wondering if alpha particles created by radioactive decay ever have enough energy to fuse with something else (e.g. hydrogen or another alpha particle).

Homework Statement The energy of an electron in a hydrogen atom is: E = p^2/2m_e - \alpha e^2/r; where p is the momentum, m_e is the electron charge magnitude, and \alpha the coulomb constant. Use the uncertainty principle to estimate the minimum momentum in terms of m_e, a, e, \hbar...

Homework Statement [/B] The time-averaged potential of a neutral hydrogen atom is given by where q is the magnitude of the electronic charge, and being the Bohr radius. Find the distribution of charge( both continuous and discrete) that will give this potential and interpret your result...

1. The way we solved this problem was proposing that the wave function has to form of ##\Psi=\Theta\Phi R## where the three latter variables represent the anlge and radius function which are independent. The legendre polynomials were the solution to the ##\Theta## part. I am having some trouble...

I'm seeing a version of the potential as -Ze^2/4πεr. My question is what exactly does the Ze^2 refer to? I think the e^2 is supposed to represent the proton and the neutron, and the Z is supposed to represent the number of protons, but I'm not sure how to read it. Does e refer to the charge...

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 )...

I am wondering and have been thinking, exactly how does the energies of hydrogen atom orbital depend on quantum numbers? I am just curious because all of what I have learned/read discusses only one-dimensional situaiton, like a particle in a box, and I want to know how it can be applied to the...

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+)

If a symmetric distribution of charge has no electric dipole moment, where does the \mu term we write in the part of the hamiltonian representing interaction with light come from? We suppose it is induced by the electric field of the light?

Homework Statement Hello! I am trying to derive the ground state enegry of a hydrogen atom, and have come to U=\frac{-mk_{0}^{2}Ze^{4}}{n^{2}\hbar^{2}} Problem is, I know there should e another factor of 2 in the denomenator because I get the ground state energy of hydrogen as being 27.145eV...

How an electron transition from lower energy state to higher energy state in hydrogen atom emits a photon?

Are there any actual numbers for electron orbital velocity in hydrogen atom?

I can tell this is simple, but I'm just not seeing it: (pages 146-147) Radial equation = d^{2}u/dp^{2} = [1 - p_{0}/p + l(l+1)/p^{2}]u Later... (having stripped off the asymptotic p^{l}e^{-p} parts) d^{2}u/dp^{2} = p^{l}e^{-p}{[-2l-2+p+l(l+1)/p]v + 2(l+1-p)dv/dp + p*d^{2}v/dp^{2}} And he...

I am working on the Hydrogen atom and I was trying to calculate \frac{d<r>}{dt} using \frac{d<r>}{dt} = \frac{i}{\hbar} <[\hat{H} , \hat{r}]>. Here r = \sqrt(x^2 + y^2 + z^2) and H = \frac{p^2}{2m} + V where p^2 = -\hbar^2 \nabla^2 . Now according to Ehrenfest's theorem <r> should behave...

Hey! I did an quantum mechanical analysis of a Hydrogen Atom in a homogeneous magnetic vector potential (I know that it might be impossible to create this kind of field) out of curiousity. I showed it to some professors of mine, but they all said that they don't have time. So I decided to post...

Homework Statement I solved the Schrödinger equation, obtaining a wave function in terms of Radial and the spherical harmonics as follows: $$Ψ(r,0)= AR_{10} Y_{00} + \sqrt{\frac23} R_{21} Y_{10} + \sqrt{\frac23} R_{21} Y_{11} - \sqrt{\frac23} R_{21} Y_{1,-1}$$ Homework Equations...

Homework Statement Calculate <p2> for ψ100 of the hydrogen atom Homework Equations ψ100 = 1/(√pi) (1/a0)3/2 e-r/a0 0∫∞ r n e-B rdr = n!/Bn+1 p2 = -hbar ∇2 = -hbar2 (r2 d2/dr2 +2 r d/dr) (ψ does not depend on ø or θ) The Attempt at a Solution<p2> = ∫ψ*(p2ψ)dV ∫dV = 4pi0∫∞r2dr <p2> =...

Homework Statement Consider the following. (a) For a hydrogen atom making a transition from the n = 4 state to the n = 3 state, determine the wavelength of the photon created in the process. (Already solved this, 1.86x10^3 nm) (b) Assuming that the atom was initially at rest...

Homework Statement Verify that the equation of the ground state energy Eo of the Bohr atom: Eo= (2pi2e4mek2)/h2 simplifies to Eo = 13.6 eV. Show clearly how the units of the different quantities in the equation simplify to the eV. This is all they give. Nothing more...

Can someone give me a link where I can find data on the size of an H atom (free and in main compounds like water)? If there is none can you tell me roughly the range of sizes or at least what is the ratio between a free atom and a bound atom. I know that for a free atom the radius is not the...

I am working through an explanation of the wave function of the Hydrogen atom. I have got as far as deriving the version of Schrodinger's equation for the one-dimensional problem in which only the radial coordinate can vary: ##[-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial^2...

Hello, I happened to open up an old book by Sah, and in it he says: "it is evident that the electron orbit radius is half the well radius at the energy level E_n" The orbit radius is r_n=\frac{4*\pi*ε_0*\hbar^2*n^2}{mq^2} and the potential well...

Homework Statement A hydrogen atom is prepared in its ground state with spin up along the z-direction. At time t = 0 a constant magnetic field ##\vec{B}## (pointing in an arbitrary direction determined by ##\theta## and ##\phi##) is turned on. Neglecting the fine structure and terms...

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...