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Arrangement of Electrons in Atoms 4-2 The Quantum Model of the Atom Electrons as Waves Last section we learned that light can behave as both a particle and a wave. What about electrons? Louis De Broglie stated that electrons could be considered waves confined to a space around an atomic nucleus. Electron waves can exist, but only at specific frequencies corresponding to specific frequencies. Electrons as Waves Experiments showed that electrons (like light) could be bent, or diffracted. Also, electron beams could interfere with each other. Diffraction – bending of light when passed through a crystal. Interference – overlapping of waves, reducing energy in some areas. Heisenberg Uncertainty Principle The position and momentum of a moving object can not simultaneously be measured and known exactly. Due to the duel nature of matter and energy Only important with small scale objects Heisenbery Uncertainty Principle Animation Chapter 4 Section 2 The Quantum Model pages 104-110 5 The Schrödinger Wave Equation Erwin Schrödinger developed an equation, which treated electrons in atoms as waves. Solutions to wave equation are known as wave functions. Don’t worry about wave functions, we do a little more with it in AP Coupled with Heisenberg Uncertainty Theory, lead to Quantum Theory Quantum Theory – describes mathematically the wave properties of The Schrödinger Wave Equation Most Important Idea: We can only know the probability of finding an electron, not its exact location. Orbital – a 3-dimensional region around the nucleus that indicates the probable location of an electron. Fig 4-11 Review Energy is quantized ( found in specific amounts) Electrons have wavelike behavior Impossible to know electron position and momentum. Can predict the probability of electron location Called the Quantum-mechanical model Probability and Orbital The density of an electron cloud is called the electron density. Higher density – more likely to find electron Lower density – less likely to find electron An orbital is the region where a given electron is likely found. There are different types of orbitals….s, p, d, f which we will talk about more later. Orbitals and Energy To describe orbitals, scientists use quantum numbers. Quantum Number – specify the properties of atomic orbitals and the properties of electrons in orbitals. Principal Quantum Number indicates the main energy level occupied by the electron. Sometimes considered the shell. n are positive integers (n = 1, n=2, n=3, …) As n increases, energy and distance from nucleus increases. n = 1 is the lowest energy level, closest to the nucleus. More than one electron can have the same value of n. The total number of orbitals that exist in a given shell is equal to n2. Angular Momentum Quantum Number (l) indicates the shape of an orbital Also considered the sublevel. The number of orbital shapes possible is equal to n l can have values of 0 and all positive integers less than or equal to n-1 If n = 1, l = 0: (l = n – 1 = 1 –1 = 0) If n = 2, l = 1 and 0: (l = n – 1 = 2 – 1 = 1) Each orbital is assigned a letter, which corresponds to a shape s orbital – see figure 4-25 pg 144 p orbital- see figure 4-26 in book d orbital – see figure 4-27 in book Each atomic orbital is designated by the principal quantum number followed by the letter of the sublevel. Ex. 1s sublevel is the s orbital is in the first main energy level Ex. 2p sublevel is the set of p orbitals in the second energy level Ex. 3d sublevel is the set of d orbitals in the third energy level Magnetic Quantum Number (ml ) indicates the orientation of an orbital around the nucleus ml = +/- l and every integer in between Ex. If n = 1, l = 0, ml = 0 This means there is a single s orbital in the first energy level If n = 2, l = 1, ml = -1, 0, +1 In the second energy level there are three p orbitals If n = 4, l = 2, ml = -2, -1, 0, +1, +2 In the fourth energy level there are five d orbitals. If n = 4, l = 0, ml = 0 In the fourth energy level there is 1 s orbital Spin Quantum Number (ms) o indicates the spin states of an electron in an orbital, either +1/2, or –1/2. Electrons spin on an internal axis either clockwise or counterclockwise. A single orbital can hold a maximum of two electrons, which must have opposite spins. Summary of Energy Levels, Sublevels, and Orbitals Principal Sublevels Energy Level n=1 1s Orbitals n=2 2s, 2p 2s (one) + 2p (three) n=3 3s, 3p, 3d 3s(one) + 3p(three)+3d(five ) 1s (one) Max Number of Electrons in Each Sublevel Sublevel # of Orbitals s 1 Max # of Electrons 2 p 3 6 d 5 10 f 7 14