23 Question 5: 50 points We have often mentioned the ferromagnetic properties of Iron as being mysterious. We learned in
Posted: Tue May 17, 2022 8:37 pm
- 23 Question 5 50 Points We Have Often Mentioned The Ferromagnetic Properties Of Iron As Being Mysterious We Learned In 1 (61.52 KiB) Viewed 46 times
- 23 Question 5 50 Points We Have Often Mentioned The Ferromagnetic Properties Of Iron As Being Mysterious We Learned In 2 (57.31 KiB) Viewed 46 times
23 Question 5: 50 points We have often mentioned the ferromagnetic properties of Iron as being mysterious. We learned in class that magnetic fields are created by moving changes, for example electrons moving around the nucleus. So what's the mystery? Let's discuss ferromagnetism (refrigerator magnets). Moving charges create magnetic fields and also respond to existing magnetic fields. Let's start with the classical model. 1) Write the equation for the force exerted by external electric and magnetic fields onto a charged particle: 2) The rate of work that a force E does on a particle is defined as Ey, where y is the velocity of the moving (test) particle. Using your answer to #1. what is E. y equal to? (Recall that axb yields a vector that is perpendicular to both a and b). What this result tells us is that the magnetic field does no work (because B does not appear in the above), so the energy of a test particle does not depend on the magnetic field. For convenience, we can set the magnetic field to vero: classically, no material should generate a magnetie field! Obviously something is wrong. The solution lies in quantum mechanics-refrigerator magnets are inherently quantum-mechanical Specifically, the explanation of ferromagnetism requires a combination of spin, the Pauli exclusion principle, and the crystal structure of Iron. 3) Write down the four quantum numbers needed to specify the state of a single bound electron. Spin' can have a value of +1/2 (for the state 1) or -1/2 (>). When a particular orbital (s.p. d....) is full, what is the total value of spin? For example, consider Helium- there are two electrons that together, fill the 1s orbital- write down the state In..m, for each electron in He, and add the value of each individual spin to get the total spin.
The spin of a single electron (approximately) generates a magnetic field B = 9.27*10" 2 [T] (for spin state T>). What is the magnetic field generated by an atom of Helium? For atoms with unfilled orbitals- most of the periodic table there is an unpaired' electron that results in a non-zero B. This is why most materials are paramagnetic. Compare the magnitude of B from a single electron to the magnetic field of the earth. To explain the ferromagnetic behavior of Iron, Cobalt, Nickel, and the few other materials that are permanently magnetic, we need one other ingredient: crystal structure, or how atoms are stacked together. Consider the spin state of unpaired electrons in two neighboring atoms, for example 111>. In this case, the neighboring atoms have unpaired spins oriented opposite to each other. It tums out that for Iron (and a few other elements) the states 11> and teach have energies 1.21*1021) (7.55*10eV) less than the energies of states 1 and 14T> Given the rule "everything is lazy", which states would neighboring Iron electrons choose to be in (if electrons could make choices)? So, Iron atoms like to point in the same direction. For example, 10 aligned Iron atoms have a total spin ofs. What's the magnitude of B produced by a mol of aligned Fe atoms? How does this compare to the magnetic field of the earth? It may seem surprising that explaining how a simple refrigerator magnet works requires such advanced Physics!