1. The energy difference between the two nuclear spin states A. is a constant. B. is...
10.28 Using equation 10.55, calculate the difference in energy between the two spin angular momentum states of a hydrogen atom in the 1s orbital in a magnetic field of 1 T. What is the wave- length of radiation emitted when the electron spin "flips"? In what region of the electromagnetic spectrum is this? The energy of the spin magnetic moment in a magnetic field B is (see equation 10.41) (10.55) 10.28 Using equation 10.55, calculate the difference in energy between...
1. List the most common nuclei that are used in NMR. 2. How many nuclear spin states are possible for the 1H nucleus? A. 1 B. 2 C. 4 D. 5 E. none of these 3. Which of the following electromagnetic radiation is used in NMR spectroscopy? A. UV B. IR C. visible D. γ-rays E. radio wave 4. _______ protons experience a net magnetic field strength that is smaller than the applied magnetic field. A. Deshielded B. Shielded C. ...
(a) If an atom with one unpaired electron spin is placed in a magnetic field B, then there are two energy levels, corresponding to the two values of the quantum number ms. Calculate the energy difference AU between the states. (b) If the atom is irradiated it will absorb energy if the frequency v=4. This is phenomenon is called electron spin resonance. Calculate the frequency if B, is 27. In what part of the electromagnetic spectrum is this frequency?
4. When an external magnetic field B is applied, a "spin-1" ion has 3 magnetic states with energies given Em=aBm, m=-1,0,1, where a is a constant of order a few times the Bohr magneton up = en/(2m). (Note: the notation here is quite different from that of Kittel & Kroemer who use "m" for the elementary magnetic moment which we have denoted a. In our terminology, m=ms is an integer quantum number: m=-1 labels the "spin down" state, m=0 labels...
2. (25 points). Rabi oscillations. Consider a spin-1/2 particle in a magnetic field B - Bo2 such that the spin eigenstates are split in energy by hwo (let's label the ground state |0) and the excited state |1)). The Hamiltonian for the system is written as hwo Zeeman - _ here and below. ơng,z are the usual Pauli matrices. A second, oscillating field is applied in the transverse plane, giving rise to a time-dependent term in the Hamiltoniain hw Rabi-...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harmonic oscillator potential with natural frequency W.Att-0 an external magnetic field is turned on which is uniform in space but oscillates with temporal frequency W as follows. E(t)-Bo sin(at) At time t>0, the perturbation is turned off. Assuming that the system starts off at t-0 in the ground state, apply time-dependent perturbation theory to estimate the probability that the system ends up in an...
If an H atom with a 1s configuration is placed in a magnetic field, the electron spin degeneracy will be removed and the number of states with different energies will be A. One B. Two C. Three D. None of the above
38) One difference between a chemical reaction and a nuclear reaction is that in a nuclear reaction a. atoms retain their identity. b. atoms often change from one element to another. c. only the valence electrons are involved. d. only small amounts of energy are absorbed or emitted. ) Ionizing radiation a. is radiation of sufficient energy to produce ions. b. is radiation of sufficient energy to remove electrons from atoms. c. is radiation of sufficient energy to produce charged...
Question 1 A system of N identical non-interacting magnetic ions of spin Y%, has energy u tHo for each spin. μο is the magnetic moment in a crystal at absolute temperature T in a magnetic field B. For this system calculate: a) The partition function, Z. b) Free energy, F. c) The entropy. S d) The average energy, U e) The average magnetic moment, M
For a spin-1/2 particle in a magnetic field B, with energies and , (a) calculate the partition function. (b) Show that the mean energy of this particle is given by ̅ For a system of noninteracting spins, (c) what is the total partition function and (d) mean energy? We were unable to transcribe this image2 2kT 2 2kT