Hydrogen atom Definition and 397 Threads

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[...

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...

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

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

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...

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}[...

Moved. Delete please.

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 =...

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...

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...

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...

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...

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?

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?

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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)}...

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...

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?

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...

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...

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 =...

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...

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...

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

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...

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...

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...

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?

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...

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?

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...

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...

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...

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...

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...

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...

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...

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.

[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 ...

[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...

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...