Hydrogen atom Definition and 410 Threads

Hi, If the normalized 1D wave-function of hydrogen atom for n=1, l=0, m_l=0; \psi_{1s}(x)=\frac{1}{\sqrt{\pi} a_{0}^{3/2}}e^{-x/a_{0}} and probability distribution of wave-function, \mid\psi_{1s}(x)^2\mid so integration of rho over all x should give the number of electrons which is equal to...

I've searched google for some decent tables but couldn't find any. I'm trying to collect Normalized Spherical Harmonics Associated Legendre Polynomials Zeros of the Spherical Bessel Function Normalized Radius Function for the Hydrogen atom etc. I'm allowed a sheet with as much of these...

Find <nlm|(1/R)|nlm> for the hydrogen atom (nlm = 211), R is just the radial position Operator (X2 + Y2 + Z2)½.

Would someone tell me some website where I can find the relativistic treatment of the hydrogen atom using Dirac's Equation? I am not trying the find the method which uses Schrodinger's equation and adds as perturbations fine and hyperfine structures? Thank you. So far i have not find anything...

What quantities appear in both the Schrodinger approach and the original Bohr theory of a hydrogen atom? Also, in what ways do the two approaches differ? I'm not sure which quantities appear in both approaches. My guess would be that it has something to do with the energy levels and angular...

A hydrogen atom is in the state \psi=Ar^2e^{-r/a}cos(\theta). I need to find lowest energy state and etc. Obviously normalize to find A, but I'm not seeing the obvious linear combination of wave functions; and I really don't think my instructor wants me to do several inner products (plus...

Here comes a pretty hard question, which not even my QM teacher has been able to answer. When we think about one hydrogen atom, and put it in an electric field along the z-axis \bar E = \bar e_z E. Then the potential for a hydrogen atom will look like this: U = -\frac{e^2}{4\pi \epsilon_0...

Hello, I don't know if this is the right place to post.. this is a self study question from Levine, it is told that is important but i have no clue in solving it .. The Balmer series corresponds to a set of emissions involving the electron in a hydrogen atom relaxing from a high energy...

The 1s radial function of the wave function of H atom is: R10=2 a-3/2e-r/a ,where a = 5.29*10-11 meter but substituting a with its value,we will get R10 = 5.2*1015 *e(-1.89036*1010 r) and that is impossible if r=a and R(r)=1.9*1015 where is the problem ? What's more, the unit...

I'm studying particle physics now and am confused with all these terminologies.

Homework Statement A Hydrogen atom is initially in its ground state and then subject to a pulsed electric field E(t)=E_{0}\delta(t) along the z direction. We neglect all fine-structure and hyperfine-structure corrections. Homework Equations 1. It is important to use selection rules to avoid...

Are there any ionizing solutions for the hydrogen atom problem, where the electron breaks away from the proton?

Homework Statement During my calculation of hydrogen atom perturbation, I need to integral below in cartesian coordinate. It is given that below integral can be transformed. Homework Equations Anyone could help to see what will the transformed integral in polar coordinate if the...

Homework Statement A hydrogen atom in the n = 2 state absorbs a photon with wavelength 380 nm. Q1. Find the change in the atom’s total energy. Q2. Find the change in the atom’s potential energy Q3. Find the change in the orbiting electron’s kinetic energy. Homework Equations...

Homework Statement A hydrogen atom is in a state with energy -0.278 eV. Homework Equations L = nh' The Attempt at a Solution The answer book says to do E_n = (-13.6 eV)/n^2 but I can't find this equation in our book. Is the 13.6 a significant number or just a different number...

Homework Statement Substitute an electron in a neutral hydrogen atom with a muon. a) calculate the Bohr radius of the ground state for this myonic atom of atom. The answer must be right to at least 2 significant digits. b) Calculate the fraction of the myon that is located inside the proton...

Homework Statement Substitute an electron in a neutral hydrogen atom with a muon. a) calculate the Bohr radius of the ground state for this myonic atom of atom. The answer must be right to at least 2 significant digits. b) Calculate the fraction of the myon that is located inside the proton...

Homework Statement Calculate the expected value for r^2 for the 2s wavefunction of the hydrogen atom (only the radial part of the function is needed for l=0). If you choose to solve this problem graphically, plot or sketch the function you integrate. Homework Equations...

You see hydrogen electron energy states labeled as 1s1/2, 2s1/2, 2p1/2 and 2p3/2. My confussion may be with understanding the definitions, but does not the 2s1/2 state imply that there are 2 electrons around as the 1st s orbital is filled. But, by definition doesn't that mean you are dealing...

lets say i have a hydrogen atom and i shoot a photon at it but the photon does not have enough energy to kick the electron to the next energy level , does the electron absorb the photon and if it does what happens ?

Hi there! If I want to find the eigenstates of the hydrogen atom in QM I start with the hamiltonian of a free particle in a Coulomb potential. But an electron in a coulomb potential is stable in classical mechanics too! The instability of the system comes from the fact that the electron...

Homework Statement What energy (in eV) is required to remove the remaining electron from a singly ionized helium atom, He+ (Z = 2)? (a) 3.40 eV (c) 27.2 eV (e) 76.9 eV (b) 13.6 eV (d) 54.4 eV Homework Equations Ei - Ef = hf The Attempt at a Solution Ef: the 1st level Ei...

Homework Statement Diagram not to scale: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy (J) n = 3 ----------------------------------------… - 0.24x10^-16 n = 2 ----------------------------------------… - 0.54x10^-18 n = 1...

1. The problem statement A hydrogen atom has an electron in the fundamental state. a. Show that a radiation with λ = 50 nm will ionize the atom. b. What will be the excess kinetic energy of the electron in joules? What is this question asking? Is it asking what wavelength will free...

Homework Statement Find the wavelength of the radiation emitted when a hydrogen atom makes a transition from the n = 6 to the n = 3 state. Give answer in µm. Homework Equations z^2 / n^2 x 13.6ev delta E = E2 - E1 = hv The Attempt at a...

The system is at the state of Φ=aY_11+bY_20 (a^2+b^2=1),please find the possible eigenfunctions of Lx and the relevant possibilities? My solution: I have attempted to use the matrix mechanics to work out the exercise,but I should work out a 8-order matrix. Firstly I use the Fmn=〈m︳F|n〉to...

1. The most probable point a 1s electron will be found in the hydrogen atom is r = 0. 2. The most probable distance that a 1s electron will be found in the hydrogen atom is r = 0. 3. For a hydrogen atom with l (lower case L) = 0, Ψ is independent of the angles Θ and Φ. 4. For a hydrogen atom...

how do i make a hydrogen atom , if i shoot an electron by a proton will it start to orbit the proton , what dictates whether it will orbit or not .

Homework Statement Comparing the hydrogen atom orbitals to an infinite square well. a.) For the hydrogen atom, what is the energy difference between the ground state and the next energy level? b.) Now 'tune' an infinite square well holding a single electron so that it has the same energy...

Homework Statement Consider a hydrogen atom whose wave function at time t=0 is the following superposition of normalised energy eigenfunctions: Ψ(r,t=0)=1/3 [2ϕ100(r) -2ϕ321(r) -ϕ430(r) ] What is the expectation value of the angular momentum squared? Homework Equations I know...

This Prob is from Shankar, 17.2.3 "we assumed that the proton is a point charge e. If the proton is a uniformly dense charge distribution of radius R, the interaction is modified as V(r)= -2(e)^2/(2R) + (er)^2/(2(R)^3) r<R = -e^2/r r>R Calculate 1st Order shift in the ground-state...

i have been working on this question for quite a while. no help on google, or my textbook at all. A hydrogen atom in its ground state is excited to the n=5 level. It then makes a transition directly to the n=2 level before returning to the ground state. A) What are the wavelengths of the...

These days I met one problem and asked a professor for help. But I can not understand his answer. Can you help me explain his answer? My question is that whether we can assume that a plane wave is orthogonal to the bound state of Hydrogen atom when t->\infty? Professor answers...

The Hamiltonian for a Hydrogen atom in Cartesian Coordinates (is this right?): \hat{H} = - \frac{\bar{h}^2}{2m_p}\nabla ^2_p - \frac{\bar{h}^2}{2m_e}\nabla ^2_e - \frac{e^2}{4\pi\epsilon _0r} In Spherical Coordinates do I just use: x=r sin θ cos φ, y = r sin θ sin φ, and z = r cos θ?

A gas composed of hydrogen atoms in the ground state is bombarded with electrons of energy 12.5eV. a) What wavelengths emitted can we expect to observe? b) If we replaced the incident electrons with incident photons of the same energy, what would happen? I know the answers to both...

Homework Statement Find the width L of a one-dimensional box for which n=5 level would correspond to the absolute value of the n=3 state of a hydrogen atom Homework Equations am i suppose to use n2h2/8mL2 where n=5 to equate it to the n=3 state of the hydrogen atom? which is -13.6eV/32...

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? E = hf = Eu - El = 2.825 eV That's the difference in energy between the initial and final states.

Homework Statement A hydrogen atom has a diameter of approximately 1.06x10^-10 m, as defined by the diameter of the spherical electron cloud around the nucleus. The hydrogen nucleus has a diameter of approximately 2.40x10^-15 m. (a) For a scale model, represent the diameter of the hydrogen...

hydrogen atom is formed by the combination of electron and proton initially separated by in finite distance ,therefore, energy of hydrogen atom is expected to be equal to loss of electrostatic potential energy,but according to quantum mechanics it is not so.Is basic energy principle violated?

I have two asks first ask : In plot of probablity density of 1s electron of hydrogen atom when r=0 where electron exist ? is inside nucleus?! how happen this second ask what is the reduis of electron ri? and what reduis of nucleos RI is ? in Hamltonain operator i mean the...

The hydrogen atom is formed by the combination of proton and electron initially separated by infinite distance therefore energy of hydrogen atom is expected to be equal to loss of electrostatic potential energy but energy value as derived by quantum mechanics is different Why is it so

. Homework Statement [/b] In a hydrogen atom the electron and proton are bound at a distance of about 0.53A. (a) Assuming the zero of potential energy at infinite separation of the electron from the proton, what is the minimum work required to free the electron? (b) What would the answer...

Homework Statement A hydrogen atom is initially in the state n=3. Subsequently it falls to its ground state with the emission of a photon. If the photon energy is ћω , then what is the ground state energy? The Attempt at a Solution I tried using E= h².n²/8ma². and got -9ћω/8 I wasn't to...

Can somebody elabroate on how the P.E. term e^2/r is thrown in shrodinger's(also Dirac) equation for the hydrogen atom by assuming such term does describe the effects of the negative and the positive charge. It enters into the equation like mass, yet quantum theory( a good one) should calculate...

Homework Statement Classical physics applied to the bohr model of the hydrogen atom would predict that light could be emitted continuously, rather than in discrete chunks of energy. Transitions between what kinds of energy levels would come close to the classical viewpoint? A. Only levels...

Let's consider eigenstates |nlm\rangle of hamiltonian of hydrogen atom. Can anyone prove that \langle r \rangle = \langle nlm|r|nlm\rangle = \frac{a}{2}(3 n^2-l(l+1)). Where a - bohr radious. I've been trying to prove it using some property of Laguerre polynomials (which are radial part...

I have been trying to picture the whole process of a photon emission by a atom. So to have good understanding what is going on, I have came up with following experimental setup. A single hydrogen atom in excited state ^2\!P_{1/2}, which has been orientated with a magnetic field so that...

Could anyone help solve a problem how to find absorption lines in hydrogen atom from n=10 (n - principal quantum number). I know that not all quantum jumps of an electron in atom are possible, thus I don't know how many different emission lins will be from this energy level where n=10.

The Hydrogen Atom wave function. With the substitution u(r) = r.R(r) p=kr We get a simplified version: d^2u/dp^2 = [1 - (p_0)/p + l(l + 1)/(p^2) ].u Im sure some of you have seen that before. Now, in the limit, p goes to infinity, I understand that we get u = A.exp[-p], but in...

I assume general relativity allows us in principle to calculate volumes of some region of space? If so, if I have a large volume of space far from other mass and energy does it make sense to ask how much a large volume of space changes depending on whether or not it contains the mass of single...