answer:
A POSITRONIUM ATOM IS A HYDROGEN-LIKE ATOM WITH POSITRON
IS (M = Me, q = +e, SPIN 1/2) AS A NUCLEUS AND BOUND ELECTRON.
11.17 A positronium atom is a hydrogen-like atom with a positron (m = meq = te,...
Consider a hydrogen atom in its ground state. The hyperfine interaction between the magnetic moment of the proton and the magnetic moment of the electron is described by the Hamiltonian: H =A S.S, where S, is the spin of the electron, S, is the spin of the proton, and A is a constant. The ground state is split by the hyperfine coupling. Obtain the energies of the split levels.
Tl 6. (4 pts) We calculated Ahf for the ground state Hydrogen atom, but now let us consider Hht for the ground state of the deuterium atom. The basic idea is the same: Here the matrix representation of S is the same, since it represents the spin operator for the spin- electron, but that of 7 is different because the deuteron is a spin-1 particle (neutron+proton) whose spin has 3 possible values for the magnetic quantum number. Also, we must...
PLEASE COMPLETE B) and stay tuned for my following 2 questions where I will ask part c) and d). Part a) has already been posted. The lowest energy state of a hydrogen-like atom has total angular momentum J-1/2 (from the l-O orbital angular momentum and the electron spin s 1/2). Furthermore, the nucleus also has a spin, conventionally labeled I (for hydrogen, this is the proton spin, 1 1/2). This spin leads to an additional degeneracy. For example, in the...
EXPERIMENT #9: SPECTRUM OF THE HYDROGEN ATOM ADDITIONAL QUESTIONS 1, What does the energy of the electron from the hydrogen atom become when n is a very large number, or approaching infinity? We say an electron with this energy has separated from the nucleus, which is now an ion. Determine the quantity of energy (AE) required to ionize an electron from its ground state in the hydrogen atom. 2. The Bohr model holds for any one-electron atom. Calculate the lowest...
P3. In a hydrogen atom in its lowest energy state (known as the ground state), the electron forms a spherically-symmetric "cloud" around the nucleus, with a charge density given by ρ-A exp(-2r a ), where a,-0.529 Â-0.529 × 10-10 m is the Bohr radius. (a) Determine the constant A. (b) What is the electric field at the Bohr radius?
10.13. (a) Consider the helium atom to be a fixed point nucleus (charge 2e) with two spin-half fermion elec trons. What is the degeneracy of its ground state? (That is, how many independent states of the whole atom have the ground state energy?) (b) Suppose instead that the electron was a spin-half boson. (It is an experimental fact that all spin-half particles are fermions, but there is nothing to stop us imagining a spin-half boson.) What then would be the...
An electron in the Hydrogen atom is in the excited state with energy E2. a) According to the Bohr model, what is the radius of the atom in this state, in Angstroms? b) What is the wavelength le of the electron, in Angstroms? c) What is the momentum of the electron, in kg-m/s ? d) This atom decays from the excited state with energy E2 to the ground state with energy E1 . What is the energy of the emitted photon?...
Consider the hydrogen atom and its eigenstates, omitting any effects of fine structure (spin- orbit coupling). For the state y21-1 give the a. expectation value of the energy b. c. expectation value of the z-component of the orbital angular momentum d. expectation value of the y-component of the orbital angular momentum e. Now replace the electron with a muon which has a mass mu200 me. What is the ratio expectation value of the total orbital angular momentum of the ground...
The Hamiltonian of the helium atom, under the assumption that the mass of the nucleus is much greater than that of the electrons and ignoring the spin, is of the form: Where are the position and momentum of the electron and is the atomic number of helium. Note that the first four terms are simply the sum of two Hamiltonians corresponding to a hydrogen atom for each electron; while the last term represents the interaction between both electrons. i) Investigate...
2. The hydrogen atom [8 marks] The time-independent Schrödinger equation for the hydrogen atom in the spherical coordinate representation is where ao-top- 0.5298 10-10rn is the Bohr radius, and μ is the electon-proton reduced mass. Here, the square of the angular momentum operator L2 in the spherical coordinate representation is given by: 2 (2.2) sin θー sin θ 00 The form of the Schrödinger equation means that all energy eigenstates separate into radial and angular motion, and we can write...