Hydrogen atom Definition and 410 Threads

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. J

    Calculating Electric Force in Bohr Model of Hydrogen Atom

    Homework Statement In the Bohr model of a hydrogen atom, what is the magnitude of the electric force exerted between the proton and the electron when the electron is in the n = 1 state? Homework Equations E= - 13.6 eV/ n^2 The Attempt at a Solution I simply...
  2. C

    Calculating Spring Constant using Minimum Energy State of hydrogen atom

    Homework Statement A hydrogen chloride molecule may be modeled as a hydrogen atom (mass: 1.67 x10^-27 kg ) on a spring; the other end of the spring is attached to a rigid wall (the massive chlorine atom). If the minimum photon energy that will promote this molecule to its first excited...
  3. L

    Superposition of states of the hydrogen atom

    say we had two states \psi1 and \psi2 and i want to model the superposition of the two states \psi=c1\psi1+c2\psi2. how do i find c1 and c2? I've been trying to do c1=\int\psi \psi1 r^2dr over the limits 0 and infinity but i don't seem to be getting anywhere. does anyone have any ideashow i...
  4. L

    Schrodingers equation for the hydrogen atom.

    hi, if p is a solution of the schrodingers equation for the hydrogen atom then is pt? (where t is the time and p is the known solution) i don't no how to do this due to the complexity of the wavefunction in the first place thanks
  5. A

    Circular Motion with a hydrogen atom

    Homework Statement In the Bohr model of the hydrogen atom, the speed of the electron is approximately 2.01e6 m/s. Find the central force acting on the electron as it revolves in a circular orbit of radius 4.84e-11 m. Answer in units of N. Homework Equations Fc=m*v^2/R The Attempt...
  6. W

    Exciting an electron in a hydrogen atom.

    Homework Statement A hydrogen atom in its ground state is illuminated with light having a wavelength of 96.7 nm. can the hydrogen atom's electron be excited to a higher energy state by absorbing one of these photons? If so, determine the state and wavelength of any photon that would be...
  7. S

    Negative Energy of Bound Bodies & Hydrogen Atom

    What is meant by total negative energy associated with bound bodies like planets. and also total energy of the hydrogen atom is negative. I wonder how it could be? Because I believe whatever negative energy may be, It must only be associated with bound systems, and I don't think that an isolated...
  8. C

    Calculating uncertainty for hydrogen atom

    Homework Statement For a object of mass m, Heisenberg’s uncertainty principle relates the uncertainty in the object’s position Δx to the uncertainty in the object’s speed Δv: (Δx)(Δv) ≥ (h divided by (4)(pi)(m)) where h is Planck’s constant. Calculate the minimum uncertainty in the speed...
  9. D

    How to calculate a commutator from hydrogen atom radial equation

    This is not homework, but is not general discussion, so not sure where this would go. In class we were deriving with the radial equations of a hydrogen atom, and in one of the equations was the commutator term: \left[ \frac{d}{d\rho}, \frac{1}{\rho}\right] my attempt was: \left[...
  10. U

    Hydrogen atom 1/r^2 expectation value

    Homework Statement Using the Feynman-Hellman theorem, determine the expectation values of 1/r and 1/r^2 for the hydrogen atom. Homework Equations Hamiltonian: H=-\frac{\hbar^2}{2m}\frac{d^2}{dr^2}+\frac{\hbar^2}{2m}\frac{l(l+1)}{r^2}-\frac{e^2}{4\pi\epsilon_0}\frac{1}{r} energy...
  11. T

    Velocity of high temperature hydrogen atom

    What is the relative velocity of two hydrogen atoms colliding head on at a temperature of 10 million Kelvin? How do you calculate this?
  12. DaTario

    Hydrogen atom as an example of perpetual motion

    Hi All, Thermodynamics forbids perpetual motion based in its second law, but how should one deal with an isolated H atom, seen here as a machine? Is there a concrete perspective of its stopping? In its stationary and fundamental state may one observe dissipation? Thank you DaTario
  13. F

    Calculating Electric Potential of a Proton in Hydrogen Atom

    Homework Statement Find the electric potential a distance of .5 x 10^-10 m from the proton of a hydrogen atom Homework Equations V= kQ/r The Attempt at a Solution I know how to answer the question, because I know which equation to use. What I do not understand is, where the...
  14. M

    Normalising phi for the Hydrogen atom.

    This is most likely very simple, but I can't figure it out. http://www.sussex.ac.uk/physics/teaching/btv/Lect02_2006.pdf Step 5 they've got an equation for \Phi. They then normalise it to get A = \frac{1}{\sqrt{2\pi}}. Every time I do the integral I get: A^2.^{2\pi}_{0}[...
  15. M

    Quick Question: Normalising phi for the Hydrogen atom.

    Moved. Delete please.
  16. I

    Calculating Magnetic Moment of Hydrogen Atom

    Homework Statement find the magnetic moment of a hydrogen atom given that the election moves at 0.10c around the nucleus and the radius is 0.5*10^-5 m Homework Equations n/a The Attempt at a Solution this is what i did. I = nev =ev (I = current e= charge of electron, v =...
  17. J

    Hydrogen atom obeying classical mechanics rather than quantum mechanics

    Suppose that the electron in the hydrogen atom obeyed classical mechanics rather than quantum mechanics. Why should such a hypothetical atom emit a continuous spectrum rather than the observed line spectrum? So far I have: quantum mechanics deals with the smallest possible piece of a system...
  18. H

    Calculating Wavelengths & Energy Levels of Hydrogen Atom

    Homework Statement the wavelengths of the emission lines produced by the hydrogen atom are given by the formula: 1/lambda = 1.096776 x 10^-2 ((1/n2^2) - (1/n1^2)) nm^-1 (a) what are the wavelengths of the first two lines in the Balmer series, H-alpha and H-beta (involving transitions...
  19. G

    Electron in a hydrogen atom (uncertainty principle)

    Homework Statement For an electron in a hydrogen atom: in state psi(100): find (del-x)(del-p) where del x = integral of :[psi (x-<x>)2 psi]dv and del p = integral of: [psi(p-<p>)2 psi]dv Homework Equations The Attempt at a Solution i attempted to multiply out both...
  20. T

    Hydrogen Atom and Relatavistic Corrections - What does this Alpha mean

    Homework Statement Okay, I need to work out the Relativistic corrections for an atom, using the First KE Term and the Darwin Term: Calculate the energy shift of the protonium groundstate due to the relativistic correction to the kinetic energy and the Darwin term and compare it to...
  21. A

    The Hydrogen Atom: An Unique Case of Quantum Numbers

    Why is the hydrogen the only atom that depends only on principal quantum number n and for all other elements, energies depend on both orbital quantum number and principal quantum number?
  22. A

    Explaining the Hydrogen Atom Wave Function Paradox

    The hydrogen atom 1s wave function is a maximum at r = 0. But the 1s radial probability density, peaks at r = Bohr radius and is zero at r = 0. can someone explain this paradox?
  23. T

    Calculating Potential of a groundstate Hydrogen Atom

    Homework Statement The groundstate energy of the hydrogen atom can be calculated using the variational principle. The normalised groundstate wavefunction is: \psi_{100} = R(r)_{10} \cdot Y_{00} with R_{10} = 2Ae^{-3/2}e^(r/a) and Y_{00} = \frac{1}{\sqrt{4z\pi}} A is the so called...
  24. L

    Mass equivalent to one hydrogen atom?

    Homework Statement If the mass of a hydrogen atom is 1.67*10-27kg and the mass of an electron is 9.1*10-31kh, how many electrons would be required to have a mass equivalent to one hydrogen atom? Homework Equations The Attempt at a Solution I tried dividing them into each other...
  25. S

    Behaviour of electron in hydrogen atom when hit by photon

    1. Given that the ground energy level of a hydrogen atom is -13.6eV, the 1st excited state -3.4eV. The difference is 10.2eV. Imagine a photon of energy 11.0eV hits the electron at ground state. What will be the final result? Electron doesn't gets excited, photo bounces off with 11.0eV? or...
  26. E

    Question about Hydrogen Atom Solution

    The last few days I've been going back to review the solution of the Schrodinger equation for the Hydrogen Atom. I learned this in school years ago and I review it every 5-10 years just to appreciate it again. However, something very basic is now bothering me, and I was hoping someone could...
  27. C

    Graphing Hydrogen atom wave functions

    Homework Statement I have a series of functions, states, and levels that I'm suppose to graph using excel. Only problem is I'm not even sure of what to do. I'm completely confused/lost. Homework Equations n=1 l=0 R(r)=\frac{2}{a_0^{3/2}}e^{-r/a_0} n=2 l=0...
  28. B

    Quantum Mechanics: total angular momentum of an electron in a hydrogen atom

    An electron in a hydrogen atom occupies the combined position and spin state. \Psi\left(\vec{r},\xi\right)=\left(\sqrt{1/3}Y^{1}_{0}\xi_{+}+\sqrt{2/3}Y^{1}_{1}\xi_{-}\right) What are the possible measured values of J^{2} (where J is the total angular momentum of the electron L + S) and...
  29. L

    Does a Hydrogen Atom Weigh Less than the Sum of Its Parts?

    Homework Statement (a) Is the mass of a hydrogen atom in its ground state larger or smaller than the sum of the masses of a proton and an electron? b) What is the mass difference? c) How large is the difference as a percentage of the total mass? d) Is it large enough to affect the value of...
  30. S

    Uncertainty principle and hydrogen atom electron

    Homework Statement Using the uncertainty principle find the energy required for the electron to be confined inside the hydrogen atom. Use the radius of the atom 1 x 10-10 m for Δr. Express your answer in eV, rounded up to the nearest hundredth. Homework Equations ΔxΔp\geqh/4pie...
  31. O

    Electric field inside hydrogen atom.

    Homework Statement A hydrogen atom can be considered as having a central point-like proton of positive charge +e and an electron of negative charge -e that is distributed about the proton according to the volume charge density rho=A*exp(-2r/a_1). Here A is a constant, a_1 = .53x10^(-10)m is...
  32. M

    Electron orbital frequency of hydrogen atom if given orbit radius

    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. A) What is the electron's orbital frequency? Homework Equations F = qE E= kq/r^2 angular velocity = v^2/r The Attempt at a Solution I'm...
  33. R

    Solving the Schrödinger equation for hydrogen atom

    Homework Statement Hello. I'd like to solve this: -\frac{\hbar^2}{2m}\nabla^2 \Psi(r,\theta,\phi) -U(r) \Psi(r,\theta,\phi) = E\Psi(r,\theta,\phi) Homework Equations The Attempt at a Solution I can separate the variables, but that's about it. \frac{1}{R(r)}...
  34. X

    Hydrogen atom ground state with zero orbital angular moment question.

    Hi all: As we know, if we solve the schrodinger equation, the ground state wavefunction is independent of theta and psi. We find the expectation value of ground state orbital angular momentum is zero. But if we don't do any mathematical calculation, can we conlude that? For example, Due to...
  35. F

    Zero point energy of hydrogen atom

    Zero point energy and hydrogen atom In quantum mechanics, the lowest energy level of Simple Harmonic Oscilator is not zero and equal to hw/2. It is called the zero point energy. Is the energy level at ground state of hydrogen atom the zero point energy also?
  36. S

    Basic treatment of the hydrogen atom through wave mechanics.

    Hey there. I'm trying to redo basic quantum chemistry with a lot more rigor. I'm currently using Pauling's "Introduction to Quantum Mechanics With Applications to Chemistry". Here is a copy of the page(s) I will be referring to...
  37. P

    Perturbation theory energy shift for hydrogen atom

    I'm trying to follow some working by lecturer; Treating delK (previously found in first bit of question), show that the energy En of the usual hydrogenic state [nlm> is shifted by some expression given. basically we start with \[ \frac{1}{2m_{0}c^{2}} \left\langle...
  38. N

    LC circuit model of hydrogen atom

    I thought these were weird similarities between macroscopic electronic circuits and (Bohr) hydrogen model. What do you guys think? . hydrogen self-capacitance (energy level "capacitance") C = 4*pi*eo*br = 5.88798e-21 Farads eo = vacuum permitivity br = Bohr Radius m = electron mass e =...
  39. J

    Consider a Hydrogen atom in the ground state

    Homework Statement Consider a Hydrogen atom in the ground state Find: A- The Kinetic Energy, in eV B - The Potential Energy, in eV C - The Total Energy, in eV D - minimum energy required to remove the electron completely from the atom, in eV E - What wavelength does a photon with the...
  40. C

    Hydrogen Atom Wavefunction Boundary conditions

    Hi, I have been given a differential equation to use in order to solve for the Hydrogen wavefunction in the ground state using Euler's method. d^2u_nl/dr^2 -(l(l+1)/r^2)*u_nl + 2k*(E_nl-V(r))*u_nl = 0 V(r) = -a/r where a = 1/137.04 I have been given initial conditions u_nl(0) = 0 an...
  41. D

    How many wavelengths could appear in the spectrum of hydrogen atom

    How many wavelengths could appear in the spectrum of hydrogen atoms initially in the n=5 state?
  42. T

    What was the energy level of the individual electron of hydrogen atom ( Η )?

    Homework Statement When a excited atom hydrogen ( wavelength ) de-energized emits energy and the electron returns to the fundamental situation. If the wavelength of the radiation emitted is 121 nm, to find what was the energy level of the individual electron of hydrogen atom ( Η ) in the...
  43. A

    Time-dependent perturbation theory: hydrogen atom in electric field

    Homework Statement A Hydrogen atom in its ground state (n,l,m) = (1,0,0) is placed in a weak electric fieldE(t) = 0 if t < 0 Eo *e^{\frac{-t}{\tau}} if t > 0E is in the positive z direction What is the probability that it will be found in any of the n=2 states at time t > 0 ? use...
  44. B

    Earth's Quantized Angular Momentum and Energy Transition in the Bohr Model?

    Homework Statement 4-16: if the angular momentum of the Earth in its motion around the sun were quantized like a hydrogen electron according to equation L=mvr=(nh)/2Π, what would Earth's quantum number be? How much energy would be released in a transition to the next lowest level? would...
  45. J

    Exploring Linear Momentum in a Hydrogen Atom Transition

    Homework Statement A hydrogen atom has its electron in the n = 2 state. The electron makes a transition to the ground state. The linear momentum of the emitted photon is E/c. If we assume conservation of linear momentum, what is the recoil velocity of the atom? Homework Equations v_n =...
  46. L

    Why is the spin of hydrogen atom 1/2 in NMR spectroscopy?

    if the electron has spin 1/2 and proton has spin 1/2, why is the hydrogen atom (which is made of the electron and proton) have spin of 1/2?
  47. B

    Ground state energy of hydrogen atom

    Hi everyone, This question is from my problem set this week in my Phys 371 class. Any help, hints or ideas would be very much appreciated! "Use the Heisenberg Uncertainty Principle to estimate the ground state energy in the hydrogen atom. Since the wave function that solves this problem is...
  48. L

    Does the hydrogen atom have a spin?

    does the hydrogen atom have a spin? since it has a proton (spin 1/2) and an electron (spin 1/2) then does they hydrogen atom have spin 1?
  49. L

    How much energy is required to ionize the hydrogen atom

    Homework Statement (a)the electric potential established by the nucleus of a hydrogen atom at the average distance of the circulating electron (r = 5.29 multiplied by 10-11 m) I solved this part using V = kq/r and got 27.2249V (b) the electric potential energy of the atom when the electron...
  50. T

    Linus Pauling's Hydrogen Atom: MVR=nh/2pi?

    I was reading Linus Pauling's "General Chemistry" when I noticed something that didn't quite fit. The angular momentum for the hydrogen atom was described as equivalent to n times h/2pi. Does anyone know why this statement is true? I've tried googling it and still can't seem to figure out how...
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