What is Hydrogen atom: Definition and 408 Discussions

A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the baryonic mass of the universe.In everyday life on Earth, isolated hydrogen atoms (called "atomic hydrogen") are extremely rare. Instead, a hydrogen atom tends to combine with other atoms in compounds, or with another hydrogen atom to form ordinary (diatomic) hydrogen gas, H2. "Atomic hydrogen" and "hydrogen atom" in ordinary English use have overlapping, yet distinct, meanings. For example, a water molecule contains two hydrogen atoms, but does not contain atomic hydrogen (which would refer to isolated hydrogen atoms).
Atomic spectroscopy shows that there is a discrete infinite set of states in which a hydrogen (or any) atom can exist, contrary to the predictions of classical physics. Attempts to develop a theoretical understanding of the states of the hydrogen atom have been important to the history of quantum mechanics, since all other atoms can be roughly understood by knowing in detail about this simplest atomic structure.

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  1. CDL

    Adiabatic Approximation in Hydrogen Atom

    Homework Statement Assume that Planck's constant is not actually constant, but is a slowly varying function of time, $$\hbar \rightarrow \hbar (t)$$ with $$\hbar (t) = \hbar_0 e^{- \lambda t}$$ Where ##\hbar_0## is the value of ##\hbar## at ##t = 0##. Consider the Hydrogen atom in this case...
  2. CDL

    I Probabilities Associated with Sudden Changes in Potential

    Hi, I have a question about calculating probabilities in situations where a particle experiences a sudden change in potential, in the case where both potentials are time independent. For example, a tritium atom undergoing spontaneous beta decay, and turning into a Helium-3 ion. The orbital...
  3. devan

    I Width of one electron shell of a hydrogen atom

    I'm quite new to quantum mechanics. I have a question, I'm coding a small game with my friends and I do understand the orbitals and I've even written a function in java to simulate the probabilities of ONE of those diagrams, but I do not know my scale just yet, can anyone tell me the width of...
  4. sumit_1

    The lifetime of the excited states of a hydrogen atom?

    How can we differentiate among the lifetimes of the excited states of the hydrogen atom? The states are: 2p, 2s, 3s, 3p
  5. Lucas Silva

    Gauss' Law: Charge of a Hydrogen Atom

    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...
  6. arupel

    I Quantum field theory and the hydrogen atom

    Quantum mechanics does a good job in describing the hydrogen atom. Are there any views either mathematically or conceptually in describing the hydrogen atom?
  7. C

    Find the relation of chemical potentials in chemical reaction In hydrogen atom ionization

    Homework Statement In hydrogen atom ionization H→p+e show that ##μ_H=μ_p+μ_r## Homework Equations G=μN (N is the number of particles) The Attempt at a Solution (1) I think the question should say "Find chemical potential relation AT EQUILIBRIUM", don't you think? (2) My professor said that...
  8. Y

    I How to factorize the hydrogen atom Hamiltonian?

    Hello, The hydrogen atom Hamiltonian is $$H=\frac{p^2}{2m} -\frac{e^2}{r}\tag{1}$$ with e the elementary charge,m the mass of the electron,r the radius from the nucleus and p,the momentum. Apparently we can factorize H $$H=\gamma +\frac{1}{2m}\sum_{k=1}^{3}\left(\hat p_k+i\beta\frac{\hat...
  9. J

    Determine energy levels of a electron in a hydrogen atom

    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...
  10. erik giles

    Light-clock and time dilation [was: Hydrogen atom expressed mathematically]

    [Note from mentor: this thread was originally posted in the Quantum Physics forum.] I am looking for a way to mathematically express the orbit of an electron around the nucleus of a hydrogen atom, while the atom is stationary as well as in motion. Note the orbit of the electron is 3...
  11. N

    Angular Momentum of a hydrogen atom in the 7f state

    Homework Statement A hydrogen atom is in the 7f state. What is the magnitude of its orbital angular momentum? Homework Equations L=sqrt(L(L+1)hbar The Attempt at a Solution L= Sqrt(3(3+1)Hbar) 1.41hbar (we want J*S) 1.41*1.054*10^-34 1.47*10^-34J*S
  12. Muthumanimaran

    Finding the probability of 1s electron within a cubical volume

    Homework Statement How to calculate the probability of finding an 1s electron within 1 picometer cubic region located 50pm from the nucleus. Homework Equations The probability of an 1s electron within a spherical volume of radius 'a' from nucleus can be find using the expression...
  13. C

    I Probability vs radial density-confusion

    Hi everyone; A very stupid confusion here. When we want to talk about the most probable radius to find the electron in $1s$ orbital, why do we talk about the radial density and not the probability itself? For instance, the probability of finding the the electron at a radial distance $r$...
  14. D

    Taylor expansion fine structure

    I have to do a Taylor expansion of the energy levels of Dirac's equation with a coulombian potential in orders of (αZ/n)^2 , but the derivatives I get are just too large, I guess there is another approach maybe? This is the expression of the energy levels And i know it has to end like this:
  15. R

    Probability of a measured energy for a hydrogen atom

    Homework Statement https://imgur.com/a/8deZc Homework Equations P(E) = ∫φ*(r)ψ(r)dr from -∞ to ∞ The Attempt at a Solution To find the probability, I know I have to use this equation: P(E) = ∫φ*(r)ψ(r)dr from -∞ to ∞ My question is, what is the energy eigenstate, φ*(r)? Is it the measured...
  16. Sophrosyne

    B The Dirac equation and the spectrum of the hydrogen atom

    I was reading that one of the successes of the Dirac equation was that it was able to account for the fine structure of some of the differences in the spectrum of the hydrogen atom. But the Dirac equation is about subatomic particles moving at relativistic velocities. But an electron around the...
  17. Erenjaeger

    I Stationary states (The Bohr hydrogen atom)

    why are energies of the stationary states negative ??
  18. Kelly Lin

    Is the Hydrogen Atom Stable for a Potential Behaving as -1/rs?

    Homework Statement An electron in a hydrogen atom does not fall to the proton because of quantum motion (which may be accounted for by the Heisenberg uncertainty relation for an electron localized in the volume with size r). This is true because the absolute value of the Coulomb potential...
  19. R

    Minimum Kinetic energy of the hydrogen atom

    Homework Statement A hydrogen atom collides with another hydrogen atom at rest. If the electrons in both atoms are in the ground state, what is the minimum kinetic energy of the hydrogen atom such that the hydrogen atom at rest will have its electron in the first excited state after collision...
  20. J

    I Electron jelly model and Hydrogen Atom

    Hi folks, I am reading "Purcell Electricity and Magnetism" and in the problem 1.77 he says: " Imagine a sphere of radius a filled with negative charge of uniform density, the total charge being equivalent to that of two electrons. Imbed in this jelly of negative charge two protons, and assume...
  21. ikihi

    A hydrogen atom transitions from n= 5 state to the ground state

    Homework Statement A hydrogen atom transitions from ni= 5 state down to the ground state. a) What is the energy of photon emitted from the transition of the hydrogen atom? b) What is the ratio of the momentum of the emitted photon to the momentum of an electron which possesses the same kinetic...
  22. T

    Deriving the ionization energy of a hydrogen atom

    Hi, I've just gotten started with basic quantum physics in physics class and we've just talked about ionization energy. It is stated that the energy of a hydrogen atom is -13.60eV (or -2.179aJ). I assume this is the potential energy (and that this is the reason the atom has a lower mass than the...
  23. Dadface

    I Virial theorem as applied to hydrogen atom

    In the virial theorem the numerical value of the average potential energy within a system is exactly twice that of the average kinetic energy. I know the theorem is proved mathematically but to me it seems a coincidence that one value is exactly twice the other value. I find that interesting. I...
  24. Cocoleia

    Normalizing the wave function of the electron in hydrogen

    Homework Statement I am having trouble with part d, where they ask me to prove that the wave function is already normalized The Attempt at a Solution But that clearly doesn't give me 1. I tried to use spherical coordinates since it is in 3D? Not really sure how to proceed. EDIT: I realize...
  25. D

    Quick question about hydrogen atom perturbation

    Homework Statement I have already solved the problem, but I don't really understand why the orbital angular momentum in the z-direction has to be taken to 0 ? Homework EquationsThe Attempt at a Solution Suppose the component of orbital angular momentum in the z-direction is...
  26. Leechie

    Perturbation of a Hydrogen atom

    Homework Statement Suppose there is a deviation from Coulomb's law at very small distances, with the mutual Coulomb potential energy between an electron and a proton being given by: $$V_{mod}(r)= \begin{cases} - \frac {e^2} {4 \pi \varepsilon_0} \frac {b} {r^2} & \text {for } 0 \lt r \leq b \\...
  27. PedroBittar

    I Extended hamiltonian operator for the Hydrogen atom

    I am familiar with the usual solution of the hydrogen atom using the associated legendre functions and spherical harmonics, but my question is: is it possible to extend the hamiltonian of the hydrogen atom to naturally encompass half integer spin? My guess is that spin only pops in naturally in...
  28. Leechie

    Calculating potential energy of hydrogen atom

    Homework Statement Calculate ##\left< \frac 1 r \right>## and ##\left< \frac 1 {r^2} \right>## and the expectation value and uncertainty of the potential energy of the electron and proton for a hydrogen atom in the given state. The given state is: $$ \psi_{2,1,-1} \left( r,\theta,\phi \right)...
  29. yecko

    Quantum number in hydrogen atom

    Homework Statement http://i.imgur.com/GQ9Xk6d.png Homework Equations Quantum mechanical model of atomic structure The Attempt at a Solution Why all sets are allowed? H atom only got one e- which only one orbital should be there, isn't it? If there aren't second or more e- , no second...
  30. Nacho Verdugo

    Normalize Hydrogen Wavefunction

    I'm trying to prove that the wave function of Hydrogen for the fundamental state is normalized: $$ \Psi_{1s}(r)=\frac{1}{\sqrt{\pi a^3}}e^{-\frac{r}{a}} $$ What I tried is this: $$ I= \int_{-\infty}^{\infty} | \Psi^2(x) | dx = 1$$ $$ \int_{-\infty}^{\infty} \frac{1}{\pi...
  31. S

    Hydrogen atom in a magnetic field

    Homework Statement A beam of neutral hydrogen atoms in their ground state is moving into the plane of the page and passes through a region of a strong inhomogeneous magnetic field that is directed upward in the plane of the page. After the beam passes through this field, in how many beams was...
  32. Y

    Potential in center of mass for Hydrogen atom

    Homework Statement A Hydrogen atom is interacting with an EM plane wave with vector potential $$\bar A(r,t)=A_0\hat e e^{i(\bar k \cdot \bar r -\omega t)} + c.c.$$ The perurbation to the Hamiltonian can be written considering the proton and electron separately as...
  33. Ian Baughman

    Electron in orbit of around a single proton

    Today I was doing some reading and I came across this topic. If we have a stationary hydrogen atom with a single electron in orbit around the nucleus and want to calculate the kinetic energy of the electron we would take the following approach. 1) Using Newton's second law: F = ma ⇒ FE = mac...
  34. M

    Solving Radial Schrodinger Equation

    Homework Statement This is a (long) multi-part question working through the various stages of solving the radial Schrodinger equation and as such it would be impractical to type it all out here but I will upload the pdf (https://drive.google.com/open?id=0BwiADXXgAYUHOTNrZm16NHlibUU) of the...
  35. M

    Where am I going wrong in my radial equation substitution derivation?

    Homework Statement Essentially we are describing the ODE for the radial function in quantum mechanics and in the derivation a substitution of u(r) = rR(r) is made, the problem then asks you to show that {(1/r^2)(d/dr(r^2(dR/dr))) = 1/r(d^(2)u/dr^2) Homework Equations The substitution: u(r) =...
  36. L

    I How many orbits are in the hydrogen atom?

    How many orbits are in the hydrogen atom?
  37. Christofferk

    Kinetic energy of the hydrogen atom in its ground state

    I saw another post about this but i didn't quite find what i was looking for there so i thought i'd give it a go instead with a thread. Homework Statement Calculate the exact value of the kinetic energy of the hydrogen atom in its ground state. No more information is given, we are referred to...
  38. Shing Ernst

    B Hydrogen Atom States Before Photon Emission | Help

    I have some confusions, and I would like some help: What states will hydrogen atom be before it emits a photon? Will it possible be superposition of its eigenstates? (If so, then by measuring the energy of photon, we measure its' energy causing its wavefunction collapse, am I right?)...
  39. J

    Hydrogen Atom: Wavefunction collapse after measurement of Lz

    Homework Statement Suppose we have a wavefunction with n=4. If we measure the orbital angular momentum along the z-direction(no spin in this problem) and get 2*hbar then what are the possible values of the total angular momentum and what is the most general wavefunction after the measurement...
  40. G

    What is the Orbit of Hydrogen Atom for an Electron at 734 km/s?

    Homework Statement On which orbit of hydrogen atom an electron has the speed of 734 km/s? Homework Equations Bohr's second postulate: mvr=nh,m=9.109\cdot 10^{-31}kg,v=734 km/s,h=6.626\cdot 10^{-34} m^{2}kg/s The Attempt at a Solution By using the second Bohr's postulate, we get 6686.006\cdot...
  41. The Bill

    I Visualizations of a hydrogen atom in an external electric field

    I'd like to see some 3D visualizations of what the wave functions of the electron and proton in a hydrogen atom would look like in different applied electric fields. Say, have a reference image at 0V, then images at various voltages where the wave functions look interesting or just illustrative...
  42. otaKu

    B Binding energy of the electron in Hydrogen atom.

    This website here says that the expression for binding energy for an electron is: This http://ocw.mit.edu/high-school/chemistry/exam-prep/structure-of-matter/atomic-theory-and-atomic-structure/MITHFH_lecnotes05.pdfby MIT calculates it quantum mechanically to give: The book I was reading...
  43. K

    Electrostatic Energy in the Hydrogen Atom

    Homework Statement We model the Hydrogen atom as a charge distribution in which the proton (a point charge) is surrounded by negative charge with the volume density of ρ = -ρ0 * exp (-2r/a0) where a0 is the Bohr radius. And ρ0 is a constant chosen such that the entire atomic distribution is...
  44. M

    I Hydrogen Atom Photon Emission Wavelength Formula

    I am trying to calculate the Lyman-alpha wavelengths of photons emitted from different hydrogen-like atoms such as deuterium and positive helium ion 4He+, using the relation 1/λ = R*|1/ni^2 - 1/nf^2|, where R is the Rydberg constant and ni and nf are integer numbers corresponding to the initial...
  45. P

    Determining <r> for the hydrogen atom

    Homework Statement The equation for the normalized ##n=3##, ##l=2##, ##m=0## wavefunction is given by $$\psi_{320}=\frac{1}{81\sqrt{6\pi}}\left(\frac{1}{a_0}\right)^{3/2}\left(\frac{1}{a_0^2}\right)r^2e^{-\frac{r}{3a_0}}(3cos^2\theta-1)e^{i\phi}$$ Determine the expectation value ##<r>##...
  46. J

    Angular momentum of hydrogen atom with Schrodinger Equation

    If we were to assume that the electron moves around the proton with radius a, the Schrodinger equation becomes: ##\frac{1}{a^2}\frac{d^2\psi}{d\phi^2} + \frac{2m}{\hbar^2}|E|\psi = 0## The question in my textbook asks me to solve the above equation to obtain values of energy and angular...
  47. P

    Excitation of a hydrogen atom by electron collisions

    The problem: A beam of electrons with kinetic energy 12.8 eV collides with a hydrogen target. What visible spectral lines will be emitted due to collisions? My question: I am confident I know how to do the bulk of this question, I am just uncertain about one thing: I know that 12.8 eV is enough...
  48. 1

    Calculate Bohr Radius of Hydrogen Atom (n=600)

    I'm doing a homework problem where it asks to calculate the diameter of a hydrogen atom with n=600. I used the equation $$r=\frac{n^2a_0}{Z}$$ where $$a_0=0.529e^{-10}m$$. Solving for r yields: $$r=\frac{(600^2)(0.529e^{-10}m)}{1}=1.90e^{-5}m$$ Multiplying by 2 to get the diameter yields...
  49. F

    Effect of spins on hydrogen atom ground state energy

    What do you think about Feynman's description (http://feynmanlectures.caltech.edu/III_12.html#Ch12-S3) ? It seems to be inconsistent with hyperphysics (http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/h21.html).
  50. Z

    What is the binding energy of H-1?

    Hello Friends ! I have a question regarding binding energy... Trying to calculate the binding energy of H-1 (hydrogen nucleus). Well it is obvious that the binding energy is zero since there is no other nucleons that the proton is bound to. But after having collected the best possible data of...
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