Week 12 Quantum PDF

QUANTUM NUMBERS OF ELECTRONS  Heisenberg Uncertainty Principle It is impossible to know simultaneously both the position and momentum (mass X velocity) and the position of a particle with certainty ! Fig. 7.15 A Radial Probability Distribution of Apples  4 Quantum Num...

QUANTUM NUMBERS OF ELECTRONS  Heisenberg Uncertainty Principle It is impossible to know simultaneously both the position and momentum (mass X velocity) and the position of a particle with certainty ! Fig. 7.15 A Radial Probability Distribution of Apples  4 Quantum Numbers Each electron has DIFFERENT 4 quantum number sets: n,l, ml and ms Quantum chemistry is based on the PROBABILITIES calculated by Heisenberg equation. According to the probabilities, 2 things can be found in the same place or 1 thing can be found at 2 places at the same time but these probabilities are very very low (but still possible).  The Bohr-Einstein Debates "God Does Not Play Dice" According to quantum mechanics, certain properties of a particle, such as its position and momentum, cannot be precisely determined simultaneously. This principle of uncertainty was a difficult concept for many physicists, including Einstein, to accept. Einstein believed that the universe was fundamentally deterministic and that God would not leave events to chance. He viewed the uncertainty inherent in quantum mechanics as a major obstacle to obtaining a complete picture of the universe. Consequently, he engaged in a prolonged debate with Bohr and other proponents of quantum mechanics. The Solvay Conferences: These debates came to a head at the Solvay Conference in Brussels in 1927. This conference brought together the most prominent physicists of the time to discuss the fundamental principles of quantum mechanics. Einstein challenged the completeness of quantum mechanics at this conference, proposing thought experiments aimed at refuting the uncertainty principle. However, Bohr was able to counter Einstein's arguments by demonstrating that his experiments did not contradict quantum mechanics. The Bohr-Einstein Debates  Quantum Computers 2 important principles Superposition of the electrons: Electrons can be found in both low and high energy states at the same time (0 and 1 at the same). Therefore, the quantum computers can run several process at the same. Entanglement (Dolanıklık) : When two electrons are at entanglement position, they can interact with each other independent of their distance. Thus, their communication may be quicker than speed of the light. Thus, this phenomenon increases the speed of communication very very dramatically. In classcial computers, speed of the clock is important (GHz). Quantum computers use the term "qubit"  Quantum Numbers - I 1) Principal Quantum Number = n Also called the “energy “ quantum number, indicates the approximate distance from the nucleus. Denotes the electron energy shells around the atom, and is derived directly from the Schrodinger equation. The higher the value of “n” , the greater the energy of the orbital, and hence the energy of electrons in that orbital. Positive integer values of n = 1 , 2 , 3 , etc.  Quantum Numbers - II 2) Azimuthal Denotes the different energy sublevels within the main level “n” Also indicates the shape of the orbitals around the nucleus. Determines s, p , d, f orbitals L=0 at s orbital ; L=1 at p orbital, L=2 at d orbital, L=3 at f orbital Positive interger values of L are : 0 to ( n-1 ) n=1 , L=0 n = 2 , L = 0 and 1 n=3,L=0,1,2  Quantum Numbers - III 3) Magnetic Quantum Number - m Also L called the orbital orientation quantum # denotes the direction or orientation in a magnetic field - or it denotes the different magnetic geometriesound the nucleus - three dimensional space values can be positive and negative (-L 0 +L) If "L = 0" , mL = 0 If "L =1" , mL = - 1,0,+1 If "L = 2" , mL = -2,-1,0,1,2  Quantum Numbers - III 4) Spin Quantum Number - m s Determines the turning direction of an electron (clockwise of counterclockwise). It can be +1/2 or -1/2 values  Four Quantum Numbers of Each Electron of Sodium Atom Electron configuration of 11 Na: 1s 2 2s2 2p6 3s1  Four Quantum Numbers of Each Electron of Sodium Atom Electron configuration of 11 Na: 1s 2 2s2 2p6 3s1 1s2 2s2 2p6 3s1 1st e 2nd e 1st e 2nd e 1st e 2nd e 1st e 2nd e 1st e 2nd e 1st e 2nd e n=1 n=1 n=2 n=2 n=2 n=2 n=2 n=2 n=2 n=2 n=3 l=0 l=0 l=0 l=0 l=1 l=1 l=1 l=1 l=1 l=1 l=0 mL=0 mL=0 mL=0 mL=0 mL=-1 mL=-1 mL=0 mL=0 mL=1 mL=1 mL=0 ms=+1 ms=- ms=+1 ms=- ms=+1 ms=- ms=+1 ms=- ms=+1 ms=- ms=+1 /2 1/2 /2 1/2 /2 1/2 /2 1/2 /2 1/2 /2  What are the quantum numbers of 11th electron of sodium atom: Electron configuration of 11Na: 1s2 2s2 2p6 3s1 1s2 2s2 2p6 3s1 1st e 2nd e 1st e 2nd e 1st e 2nd e 1st e 2nd e 1st e 2nd e 1st e 2nd e n=1 n=1 n=2 n=2 n=2 n=2 n=2 n=2 n=2 n=2 n=3 l=0 l=0 l=0 l=0 l=1 l=1 l=1 l=1 l=1 l=1 l=0 mL=0 mL=0 mL=0 mL=0 mL=-1 mL=-1 mL=0 mL=0 mL=1 mL=1 mL=0 ms=+1 ms=- ms=+1 ms=- ms=+1 ms=- ms=+1 ms=- ms=+1 ms=- ms=+1 /2 1/2 /2 1/2 /2 1/2 /2 1/2 /2 1/2 /2  What are the quantum numbers of 9th electron of sodium atom: Electron configuration of 11Na: 1s2 2s2 2p6 3s1 1s2 2s2 2p6 3s1 1st e 2nd e 1st e 2nd e 1st e 2nd e 1st e 2nd e 1st e 2nd e 1st e 2nd e n=1 n=1 n=2 n=2 n=2 n=2 n=2 n=2 n=2 n=2 n=3 l=0 l=0 l=0 l=0 l=1 l=1 l=1 l=1 l=1 l=1 l=0 mL=0 mL=0 mL=0 mL=0 mL=-1 mL=-1 mL=0 mL=0 mL=1 mL=1 mL=0 ms=+1 ms=- ms=+1 ms=- ms=+1 ms=- ms=+1 ms=- ms=+1 ms=- ms=+1 /2 1/2 /2 1/2 /2 1/2 /2 1/2 /2 1/2 /2  What are the quantum numbers of 26th electron of iron atom: Electron configuration of 26Fe: 1s2 2s2 2p6 3s2 3p6 4s2 3d6 3d6 1st e 2nd e 1st e 2nd e 1st e 2nd e 1st e 2nd e 1st e 2nd e n=3 n=3 n=3 n=3 n=3 n=3 l=2 l=2 l=2 l=2 l=2 l=2 mL=-2 mL=-2 mL=-1 mL=-0 mL=1 mL=2 ms=1/ ms=- ms=1/ ms=1/ ms=1/ ms=1/ 2 1/2 2 2 2 2 What are the quantum numbers of 33rd electron of Br atom: Electron configuration of 35Br: 1s2 2s2 2p6 3s2 3p6 4s2 3d104p5 4p5 1st e 2nd e 1st e 2nd e 1st e 2nd e n=4 l=1 ml=-1 ml=-1 ml=0 ml=0 ml=1 ms=1/ 2 What are the quantum numbers of 35th electron of Br atom: Electron configuration of 35Br: 1s2 2s2 2p6 3s2 3p6 4s2 3d104p5 4p5 1st e 2nd e 1st e 2nd e 1st e 2nd e n=4 n=4 l=1 l=1 ml=-1 ml=-1 ml=0 ml=0 ml=1 ms=- ms=1/ 1/2 2