Spin of electron and proton
- 1. S P I N O F E L E C T R O N & P R O T O N By Ayesha Anum and Marwa Batool
- 2. Spin in Quantum Mechanics - Intrinsic angular momentum associated with elementary particles. - Purely quantum mechanical phenomenon without any analog in classical physics. - Not associated with any rotating internal parts of elementary particles. - Intrinsic to the particle itself. - The concept of spin was introduced in 1925 by Ralph Kronig, and independently by George Uhlenbeck and Samuel Goudsmit.
- 3. Spin in Quantum Mechanics - Spin is quantized. - Only takes on discrete values - Spin angular momentum of an electron can only take on the values ħ/2 or -ħ/2. - Denoted by S - Its component along the z-axis by Sz. - Eigenvalues of the square of the magnitude of the spin operator are S2 = s(s+1)ħ2 - Eigenvalues of the Sz: msħ. - For the electron s = 1/2 and S2 = (3/4)ħ2
- 4. Introduction of Electron Spin: - Quantum property of electrons. - A form of angular momentum. - Magnitude of this angular momentum is permanent. - Spin is a fundamental, unvarying property of the electron. - Often explained by relating it to the earth spinning on its own axis every 24 hours as an example.
- 5. In 1920, Otto Stern and Walter Gerlach designed an experiment, which unintentionally led to the discovery that electrons have their own individual, continuous spin even as they move along their orbital of an atom. Discovery of Electron spin
- 6. Discovery of Electron spin - Silver which was put in an oven and vaporized. - Result: Silver atoms formed a beam that passed through a magnetic field in which it split in two. - Electron has a magnetic field due to its spin. - When electrons with opposite spins are put together, there is no net magnetic field because the positive and negative spins cancel out. - Silver atom used has a total of 47 electrons, 23 of one spin type, and 24 of the opposite. - Because electrons of the same spin cancel each other out, the one unpaired electron in the atom will determine the spin.
- 7. The potential energy of the electron spin magnetic moment in a magnetic field applied in the z direction is given by: Using the relationship of force to potential energy gives:
- 8. What is Electron Spin? Electron spin is articulated as: The spin quantum number can be articulated as: The total angular momentum s is articulated by: Where, the reduced Planck’s constant is ℏ and ℏ = h/2π.
- 9. - The electron spin theory shows the electron as a simple sphere, depicts it as a quantum particle. - Provides information on the direction of electron spin. - Explains its impact on certain features like the magnetic properties of the atom Electron spin theory:
- 10. Types of Electron Spin Direction 1. Spin up 2. Spin down - Spinning in the +z or –z direction corresponds to the spin up and spin down directions. - These spins relate to particles with a spin of 1/2, such as electrons. - An electron can be compared to a tiny magnetic bar in quantum theory. - Spin points of an electron can be compared to the north pole of a minute bar. - The production of a magnetic field by two adjacent electrons with comparable spin directions enhances each other.
- 11. STEPS OF IDENTIFY ELECTRON SPIN Calculating the number of electrons in an atom Drawing the electron arrangement of an atom. For this aim, one can look at the electronic configurations for further information. Using up and down arrows to represent the direction of the electron spin while distributing the electrons.
- 12. Assigning Spin Direction Restrictions apply when assigning spin directions to electrons, so the following Pauli Exclusion Principle and Hund's Rule help explain this.
- 13. - The Pauli Exclusion Principle declares that there can only be a maximum of two electrons for every one orientation. - Two electrons must be opposite in spin direction - This means one electron has ms=+1/2 and the other electron has ms=−1/2. 1. Pauli Exclusion Principle:
- 14. 2. Hund's Rule: - Hund's Rule declares that the electrons in the orbital are filled up first by the +1/2 spin. - Once all the orbitals are filled with unpaired +1/2 spins, the orbitals are then filled with the -1/2 spin.
- 15. Applications of Electron Spin Electron Spin Resonance: “Method for studying materials that have unpaired electrons.” First discovered by Yevgeny Zaviosky in 1944.
- 16. Working Principle of ESR: - Basis: Electron is a charged particle. - Spins around its axis acting like a tiny bar magnet. - A molecule with an unpaired electron is placed in a strong magnetic field. - Spin of unpaired electron can align in two different ways creating two spin states ms = ± ½. - The alignment can either parallel to the magnetic field which corresponds to the lower energy state ms = – ½ or antiparallel to the direction of the applied magnetic field ms = + ½
- 17. Working Principle of ESR: - The two alignments have different energies and - This difference in energy lifts the degeneracy of the electron spin states. - The energy difference is given by: ΔE=hν=geβBB0 Where, h = Planck’s constant v = the frequency of radiation ßB = Bohr magneton B0 = strength of the magnetic field ge = the g-factor
- 18. Applications of ESR To study transition metals containing metalloproteins. To determine the rate of catalysis. To know about the active site geometry. To study denaturation and protein folding
- 19. Spin of a Proton Introduction of Proton: - Stable subatomic particle with symbol p - H+, or 1H+ with a positive electric charge of +1 e elementary charge. - Consists of three quarks bound together by a field of gluons. - A quark is a type of elementary particle and a fundamental constituent of matter. - A gluon is an elementary particle that acts as the exchange particle for the strong force between quarks. Proton Spin Crisis: - A theoretical crisis precipitated by an experiment in 1987. - tried to determine the spin configuration of the proton. - The experiment was carried out by the European Muon Collaboration (EMC). - The main question in the proton spin crisis is where does the spin of the proton come from?
- 20. Background: - A proton has two up quarks and one down quark, and they're held together by gluons: - Ruling hypothesis: Since the proton is stable, then it exists at the lowest possible energy level. - Therefore, it was expected that the quark's wave function is the spherically symmetric s-wave with no spatial contribution to angular momentum. - Proton is a spin 1/2 particle. - Therefore, it was hypothesized that two of the quarks have their spins parallel to the proton and the spin of the third quark is opposite.
- 21. Experiment - The proton has a spin of ħ/2, or “spin-1/2” and so do each of its three quarks. - Summing the spins of the quarks to get the total spin of the proton seems straightforward. - If two of the quark spins point up and other points down, the down spin will cancel one of the ups, and both sides of the equation will be ħ/2. - With two up quarks in the ground state, we expect Pauli exclusion principle to prevent the two identical particles from occupying the same state, and so one would have to be +1/2 while the other was -1/2. - Therefore, the third quark should give a total spin of 1/2. - The experiments came, and when you smashed high-energy particles into the proton, the three quarks inside (up, up, and down) only contributed about 30% to the proton's spin.
- 22. There are three good reasons that these three components might not add up so simply. 1. The quarks aren't free but are bound together inside a small structure: the proton. 2. The gluon spin can effectively "screen" the quark spin over the span of the proton, reducing its effects. 3. There are quantum effects that delocalize the quarks, preventing them from being in exactly one place like particles and requiring a more wave-like analysis. These effects can also reduce or alter the proton's overall spin. In other words, that missing 70% is real.
- 23. NEW DISCOVERY - To see how gluon contributes to the spin of a proton, there are two ways to test: experimentally and theoretically. 1. EXPERIMENTALLY: - We can collide particles deep inside the proton and measure how the gluons react. - Gluons that contribute the most of the proton’s overall momentum contribute substantially to the proton’s angular momentum about 40% with an uncertainty of ±10%. - With better experimental setups, we could probe down to lower momentum gluons, achieving even greater accuracies.
- 24. 2. THEORETICALLY : - A calculation technique known as the lattice QCD has been steadily improving over the past few decades. - Lattice QCD can predict that the gluon contribution to the proton’s spin is 50% . - The calculations show that with this contribution the gluon screening of the quark spin is ineffective. - The remaining 20% must come from orbital angular momentum where gluons and even virtual pions surround the three quarks since the sea quarks have a negligible contribution. - With 70% of proton’s spin coming from gluons and orbital interactions, and with experiments and lattice QCD calculations improving hand-in-hand we are finally closing in on exactly why proton “spins” with the exact value that it has.
- 25. Practical uses of Electron Spin Nuclear magnetic resonance (NMR) Magnetic resonance imaging (MRI) Electron spin resonance spectroscopy Giant magnetoresistive (GMR) drive head technology. Computer memory Medical imaging Chemical spectroscopy