a) Average energy per spin is given by
where,
hence, we get
b) Entropy is given by the relation
where,
thus, the entropy is
A one-dimensional array of 1279128 noninteracting binary spins, each of magnetic moment 0.074 eV/T, are placed...
The system, which consists of N spins, each of which has a magnetic moment of μo and a spin quantum number of 1/2, is placed within the B magnetic field. Find the expression that gives the chemical potential (μ (T)) by using the expression that gives the state of the system's input (hint: use Ω(N,n)=Ω(N,0)*e^(-2n^2/N) to find the states of the system.)
Consider one dimensional lattice of N particles having a spin of 1 /2 with an associated magnetic moment μ The spins are kept in a magnetic field with magnetic induction B along the z direction. The spin can point either up, t, or down, , relative to the z axis. The energy of particle with spin down is e B and that of particle with spin up is ε--B. We assume that the system is isolated from. its environment so...
2. Interacting Spins (5 points each part, 30 points total). Two spins, each of which can be in one of two states, up or down, are in equilibrium with a heat reservoir at temperature t. They interact as follows: When the two spins point in the same direction, their interaction energy is – J, and when they point in opposite directions, their interaction energy is J. The spins also each have a magnetic moment m and are subject to a...
An electron of magnetic moment υ = γ S is placed in a magnetic field B = (-ωx/γ, -ωy/γ, -ωz/γ). Show that the evolution operator of the spin is U(t,0) = exp(-iυt)
An iron atom has a magnetic dipole moment of about 1.8 x 10-23 A · mº Part A Determine the dipole moment of an iron bar 9.2 cm long, 12 cm wide, and 1.8 cm thick, if it is 100 percent saturated Express your answer using two significant figures. 170 A mO O ? A m2 Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining Part B What torque would be exerted on this bar when placed...
A 19-cm-diameter circular loop of wire is placed in a 0.95-T magnetic field. Part A When the plane of the loop is perpendicular to the field lines, what is the magnetic flux through the loop? Express your answer to two significant figures and include the appropriate units. DU НА ? Value Wb Submit Request Answer Part B The plane of the loop is rotated until it makes a 37° angle with the field lines. What is the angle in the...
The energy of a magnetic moment in a magnetic field is . A certain paramagnetic salt contains 1025 magnetic moments per m3. Each one has a value , due to the atom's spin. As the spin is 1/2, there only are two possible states and the magnetic moments can be parallel or antiparallel to the field. Each magnetic moment belongs to one distinguishable atom. A 1 cm3 sample of this salt is placed in a electromagnet producing a uniform magnetic...
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...
Parts B, C D, E Rules for Orbital Angular Momentum Constants Periodic Table Part A Learning Goal How many different values of I are possible for an electron with principal quantum number n Express your answer as an integer To understand and be able to use the ruiles for determining allowable orbital angular momentum states 52 Several numbers are necessary to describe the states available to an electron in the hydrogen atom. The principal quantum number n determines the energy...