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. N

    How to Find Energy Corrections for a Perturbed Hydrogen Atom?

    Homework Statement A hydrogen atom is perturbed with the potential V(r) = \frac{\alpha}{r^{2}} (\alpha is small). Find first-order perturbation corrections to the energy levels and then exact levels of the perturbed system. Homework Equations The unperturbed hydrogen atom radial...
  2. M

    Hydrogen Atom Hamiltonian & Schroedinger Equation

    the Hamiltonian for the hydrogen atom appears as H= (Pr)^2/2m+(L^2)/2mr^2-e^2/r The Schroedinger equation is ((Pr)^2/2m+(L^2)/2mr^2-Ze^2/r+|E|)PHI=0 |E| because we're looking for bound states. m - reduced mass. the radial equation is...
  3. G

    Compute the main free path of a hydrogen atom in interstellar space

    Problem: Interstellar space has an average temperature of about 10K and an average density of hydrogen atoms of about one hydrogen atom per cubic meter. Compute the main free path of a hydrogen atom in interstellar space. Take the diameter of an H atom to be 100 pm. Here is what I did. I...
  4. V

    Electric Field Inside a Hydrogen Atom

    Homework Statement A hydrogen atom is made up of a proton of charge + Q=1.60 \times 10^{ - 19}\; {\rm C} and an electron of charge - Q= - 1.60 \times 10^{ - 19}\; {\rm C}. The proton may be regarded as a point charge at r=0, the center of the atom. The motion of the electron causes its charge...
  5. T

    Hydrogen Atom (this is not chemistry)

    Homework Statement A rather simplistic model of the hydrogen atom has a single electron revolving around a nuclear proton with an orbital radius of 5.40E-9 m at a speed of 5.00E+6 m/s. Determine the magnetic field at the proton due to the electron. Homework Equations B=u0*I/2piR I=Q/t...
  6. C

    Polarizability of a single hydrogen atom

    Homework Statement the problem text is attached Homework Equations The Attempt at a Solution I have solved Schrödingen equation, while getting psi(x)=c1*cos(kx)+c2*sin(kx), where k=sqrt(2Em)/hbar I cannot understand which boundary conditions I schould use.
  7. N

    Hydrogen atom (finding electron probability)

    [SOLVED] Hydrogen atom (finding electron probability) Homework Statement For electron in eigensate of Hydrogen we have these expectation values <r>= 6a , <r^-1>= 1/4a (a is Bohr radius) a) find that eigenstate. b) find the probability of finding electron in region 0 < phi < Pi/6 ...
  8. J

    Calculating Electric Field & Dipole Moment of Electron in Hydrogen Atom

    Homework Statement OK I really would appreciate some help on this - just a point in the right direction would be great: The potential due to the electron in a hydrogen atom at distance r from the nucleus is V = kq[(exp(-2r/a) - 1)/r + (exp(-2r/a)/a] Where k=1/(4pie0) where e0 is the...
  9. M

    Electrostatic Force of a hydrogen atom

    [SOLVED] Electrostatic Force Homework Statement One model of the structure of the hydrogen atom consists of a stationary proton with an electron moving in a circular path around it.The orbital path has a radius of 5.3x10^-11m. The masses of a proton and an electron are 1.67x10^-27kg and...
  10. U

    A hydrogen atom in a weak time-dependent perturbation

    Homework Statement A hydrogen atom, which is in its ground state 1s (i.e. \|1,0,0\rangle), is put into a weak time-dependent external electric field, which points into the z direction: \boldsymbol{E}(t,\boldsymbol{r}) = \frac{C\hat{\text{\boldsymbol{e}}}_{z}}{t^{2}+\tau^{2}}, where C and...
  11. E

    Solving the Hydrogen Atom Wavefunction Puzzle

    [SOLVED] hydrogen atom Homework Statement My book says that R_{1,0}(r) = 2(1/a_0)^{3/2} e^{-r/a_0} is a normalized wavefunction. But if you integrate R_{1,0}(r)^2 over r from 0 to infinity, you do not get 1. What's wrong here?Homework Equations The Attempt at a Solution
  12. S

    Calculating p^2/2m and -e^2/r for Hydrogen Atom in 3D

    Homework Statement I have a question on my quantum pset relating to calculating <p^2/2m> and <-e^2/r> for the first two spherically symmetric states of the hydrogen atom (in 3D). The Attempt at a Solution I started out trying to calculate the averages with \psi ... something like, for...
  13. E

    What is the ratio of energies in a hydrogen atom and how can it be calculated?

    [SOLVED] Energies of a Hydrogen Atom 1. I have a question on the ratio of energies of an electron in a hydrogen atom. It seems quite simple, but yet seem to be struggling...can anyone help? 2. The question is: "calculate the most probable value of the electron-orbit radius, r, and the ratio of...
  14. S

    Determine the most probable radius for a 2s orbital (Hydrogen atom)

    Homework Statement Determine the most probable radius for a 2s orbital (Hydrogen atom) Homework Equations Wavefunction for a 2s orbital: 1/(4√2pi*a^(3⁄2) ) (2-r⁄a) e^((-r)⁄(2a)) where, a=bohr radius The Attempt at a Solution First step: find the probability density by...
  15. F

    Hydrogen Atom Spin Orbit Coupling

    hi guys,could anyone please help with this question? How many levels will n=4 hydrogen atom split into due to the spin orbit coupling? i know J = L + S i don't know if i have understood the concepts properly - i know if n = 1,2,3...
  16. E

    Solving Hydrogen Atom Equations for l & a and Finding Energy]

    Homework Statement Find the values of l and a for which the function R(r) = Cexp[-r/a], where C and a are constants, is a solution of the radial equation for the hydrogen atom. Then find the energy in terms of the rydberg constant and the magnitude of the angular momentum. Finally state...
  17. B

    Calculating the energy of a hydrogen atom

    Homework Statement A sample of hydrogen atoms are all in the n=5 state. If all the atoms return to the ground state, how many different photon energies will be emitted , assuming all possible transitions occur? Homework Equations possible equation: E= hc/lambda =(E(initial) -E(final))...
  18. 2

    Electron and proton separation in a hydrogen atom

    1) Hydrogen’s electron and proton are separated by 5.3x10-13 meters. What is the electrical force between them? 2) A charge moved .02 meters in an electric field of force 215 N/C. If the electric potential decreased by 6.9x10-19, what is the charge of the particle? 3) If a capacitor...
  19. P

    Calculating Kinetic Energy of Recoiling Hydrogen Atom

    Homework Statement A hydrogen atom at rest in the laboratory emits the Lyman radiation. (a) Compute the recoil kinetic energy of the atom. (b) What fraction of the excitation energy of the n = 2 state is carried by the recoiling atom? (Hint: Use conservation of momentum.) Homework...
  20. P

    Initial and final state of hydrogen atom

    Homework Statement given the wavelength of photon absorbed by H atom and wavelength of photon emitted by that H, find the final "n" state of H atom. Homework Equations E=nhf The Attempt at a Solution I tried... n1hf1=n2hf2 n1f1=n2f2 where n1=1 so: f1=n2f2...
  21. Y

    Classical nature of the hydrogen atom

    Homework Statement According to the classical nature of the hydrogen atom an electron in a circular orbit of radius 5.3*10^-11m around a proton fixed at the centre is unstable. If it is true, how long would it take for the electron to collaspse into the proton? Homework Equations There...
  22. V

    Initial and final states of hydrogen atom

    Homework Statement A hydrogen atom in an excited state emits a photon of wavelength 95nm. What are the initial and final states of the hydrogen atom? [Hint: you will need to make a reasonable guess of what is the final state. look at the energy of the photon and compare this energy with all...
  23. C

    Energy levels for the Hydrogen Atom

    Hello everybody. As you surely know, the Schodinger treatment of the Hydrogen Atom gives wrong eigenvalues for the Spectrum. The Dirac equation provides for a correct one. On the other hand, the first who found the correct expression for the levels was "mighty" Sommerfeld using a mixture of...
  24. B

    Magnetic Moments of Hydrogen Atom in 2T Magnetic Field

    Homework Statement Consider the Hydrogren atom in a magnetic field of 2T. If the atom is in the ground state (orbital angular momentum L=0) a) Write down the magnetic moments of the proton and the spinning electron b) What is the splitting of the energy of the ground state in eV due to the...
  25. C

    Minimum Collision Speed for Excitation of Hydrogen Atoms

    Two hydrogen atoms, both initially in the ground state, undergo a head on collision. If both atoms are to be excited to the n=2 level in this collision, what is the minimum speed each atom can have before the collision? Ke = 8.99 *10^9 e = 1.602 *10^-19 ħ = 1.05 * 10 ^-34 Mass of electron =...
  26. Q

    Hydrogen atom in plane wave electronic field

    We just consider one dimensional case and the classical method. Then the motion equation of the electron in Coulomb field and the plane wave electronic field is d^2 x/ dt^2=-1/x^2+cos t. (x is the coordinate and t is the time. ) How to solve the equation exactly? We don't consider such cases...
  27. K

    Hydrogen Atom Emission and Absorption

    QW Why does the emission from hot hydrogen atoms consist of the Lyman, Balmer and Paschen series but the absorption of cold hydrogen atoms consists of just the Lyman series? is it because the cold hydrogen atoms absorb characteristic frequencies and the lyman series involves transitions that...
  28. L

    Exploring the Hydrogen Atom - Molu's Questions

    Hi, I had a few questions about the most well behaved of atoms. 1) Solving the Schroedinger equation gives us a basis (say the energy eigenstates) such that all possible wavefunctions can be written as a linear combination of these stationery solutions. This means that the system is not...
  29. F

    The Bohr Model of the Hydrogen Atom

    The electron in a hydrogen atom is in the first excited state, when the electron acquires an additional 2.86 eV of energy. What is the quantum number n of the state into which the electron moves? I found the answer to be 5 but I don't know how. I thought I could use the following equation...
  30. N

    Could you pls advise me any books where in detail is described Hydrogen atom

    Dear PF, Could you pls advise me any books where in detail is described Hydrogen atom (relativisticaly). Thank you very much.
  31. S

    Does Bohr's model of Hydrogen atom violate the uncertainty principle?

    In what ways does Bohr's model of Hydrogen atom violate the uncertainty principle?
  32. D

    Find the Central Force on an Electron in a Hydrogen Atom

    In the Bohr model of the hydrogen atom, the speed of the electron is approximately 1.96e+6 m/s. Find the central force acting on the electron as it revolves in a circular orbit of radius 4.8e-11 m. Answer in units of N.
  33. G

    Solution of hydrogen atom : legendre polynomials

    I was messing around with the \theta equation of hydrogen atom. OK, the equation is a Legendre differential equation, which has solutions of Legendre polynomials. I haven't studied them before, so I decided to take closed look and began working on the most simple type of Legendre DE. And the...
  34. A

    What Happens to the Effective Potential in a Hydrogen Atom for l>0 and r<r(min)?

    Basic SE, Hydrogen atom I'm given the basicc equation for the effective potential I've worked out the bohr radius (a) Q. Describe what happens to the effective potential for orbital angular momentum l>0 and electron radius r < r(min) r(min) = l(l+1)a I'm thinking that the effective...
  35. A

    How many degenerate quantum states are there in the 3d state of a hydrogen atom?

    In the hydrogen atom, an electron is in the 3d state. (i) Find the orbital angular momentum of the electron (in units of n =3, l = n - 1, l = 1. L = [sqrt( l (l + 1) )]hbar therefore L = sqrt(2).hbar (ii) Find the energy of the electron (in eV). En = -13.6ev / n^2. E = - 13.6eV / 9 (iii)...
  36. A

    Quantum Mechanics: Hydrogen atom in an Electric field

    So, we have an external electric field E_{ex} being subjected to a hydrogen atom and thus adding the following term to the perturbation: H^{'} = -e\vec{E_{ex}} \cdot r. The first question asks to find the correction to the energy treating it as a perturbation, and hints to use the external...
  37. R

    How do you know that there's an electron in the hydrogen atom?

    Among the reasons for asking this nominally "no-brainer" question is that it touches directly upon the notion of virtual particles. So, how do we know there's that tiny little electron in a hydrogen atom -- and, since we know there is one there, is the electron real or virtual? Regards...
  38. M

    Probability of transition in hydrogen atom

    Here's the question... A hydrogen atom is in the ground state at time t = 0. At this time an external electric field of magnitude E(t)=E*exp(-t/tau) is applied along the z direction. Find the first-order probability that the atom will be in the 210 (nlm) state at time t >> tau, assuming that...
  39. Z

    About wavefunctions of Hydrogen atom

    Every one knows that wavefunctions are generally complex functions described by three quantum numbers n, l and m, and the number m is included in the form exp(i*m*fai). But here in the following webpage they are all real functions, I'm confused:confused: . Can anyone help me? Thank u in advance!
  40. Reshma

    Normalization constant for Hydrogen atom

    Help, I'm losing it :cry:. Wavefunction of Hydrogen atom in the ground state is: \Psi (r) = Ae^{-r/r_0} Determine A. I set about trying to obtain the Normalization factor. \int \Psi^2 (r) dV = 1 \int \left(A^2 e^{-2r/r_0}\right)(4\pi r^2)dr = 1 What limits should I take for this integral?
  41. B

    Applications of Gauss's Law for a hydrogen atom

    First could someone actually explain the following question to me! Consider a hydrogen atom to be a positive point charge e at the center of a uniformly charged sphere of radius R and with total charge -e. Using Gauss' Law, find an expression for the electric field as a function of the...
  42. F

    Calculating Energy of Electron in Bohr Hydrogen Atom

    5. The energy En of an electron at the nth orbit in the hydrogen atom is given as: En = - (13.6 / n2 ) eV where n = 1,2,3, . . . . . a, If an electron is at n=3, how many spectral transition lines are possible if it falls to the ground ? For part a, what does it mean by "how many...
  43. B

    A hydrogen atom in uniform electric field

    Assume there's a hydrogen atom. Its proton(charge +e) is at the center of a spherical electron cloud(-e) which radius is 10Å and the electrons are uniformly distributed at the sphere's surface. If we now put it into a uniform electric field E_0, what is the distance \delta between the proton...
  44. C

    Calculating Work Done to Bring Proton to Hydrogen Atom Nucleus

    A hydrogen nucleus has a radius of 1 x 10-15 m and the electron is about 5.4 x 10-11 m from the nucleus. Assume the hydrogen atom is a ball with a radius of about 5.4 x 10-11 m and the nucleus is a ball with a radius of 1 x 10-15 m. How much work (in electron volts) must be performed by an...
  45. A

    Normalizaed wave function of the hydrogen atom

    how do you find the normalized wave functions of the hydrogen atom for n=1, l=0 and ml=0? in my textbook, it's a table, but i have no idea where the figures come from...
  46. A

    Finding Bohr Orbit's Quantum # for 0.01mm Hydrogen Atom

    hydrogen atoms in states of high quantum number have been created in the labortatory and observed in space. Find the quantum number of the Bohr orbit in a hydrogen atom whose radius is 0.01mm. my problem: n=(0.00001/(5.29*10^-11))^(1/2)=434.7 i think that n should be 434, because the...
  47. B

    Solving Ground State of Hydrogen Atom QM Problem

    Hi guys I'm having a problem with calculations involving the ground state of the hydrogen atom. My main issue comes from the wavefunction of this state: i.e. \Psi(r) = \frac{1}{\sqrt{\pi a^3}}\exp{\frac{-r}{a} My main problem seems to come from the fact that this function has no complex...
  48. J

    Calculate the change in energy of the hydrogen atom

    7. A hydrogen atom makes an electronic transition from its n = 4 level to its lowest energy level. Calculate the change in energy of the hydrogen atom. E = (-2.18 x 10^-18 J) (1/1 -1/16) + 2.04378 x 10^-18 J Is this correct. If not, can you show me how to do it. Thanks for the help.
  49. P

    Electron in Hydrogen Atom - De broglie wavelength

    I had a physics exam today in which we were presented with a model of a hydrogen atom with a single electron orbiting a single proton. We were told the radius of the "orbit" of the electron, and subsequently had to calculate the electrostatic force between the proton and the electron and the...
  50. S

    Electric Current in a Hydrogen Atom

    This selection comes from the Serway . Beichner, Physics for Scientists and Engineers text that many undergrads are (I'm sure) familiar with! I've looked at this problem on 3 different casual occasions and on one test and still have yet to arrange the concept in my mind... "In the Bohr...
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