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ELECTRONS IN ATOMS Chapter 5 Section Overview • 5.1: Models of the Atom • 5.2: Electron Arrangement in Atoms • 5.3: Physics and the Quantum Mechanical Model MODELS OF THE ATOM Section 5.1 The Development of Atomic Models • Atoms consist of protons, neutrons, and electrons. • Rutherford’s atomic model could not explain the chemical properties of elements. • More models were needed that explained the behavior of electrons within atoms. The Development of Atomic Models The Bohr Model • Bohr proposed that an electron is found only in specific • • • • circular paths, or orbits, around the nucleus. Each electron orbit in Bohr’s model has a fixed energy. The fixed energies an electron can have are called energy levels (ex. Rungs in a ladder: lowest rung equals lowest energy level. People cannot move between rungs, electrons cannot move between energy levels). A quantum of energy is the amount of energy needed to move an electron from one energy level to another. Bohr’s model provided more insight, but still failed to explain the energies absorbed and emitted by atoms with more than one electron since he only used hydrogen in his experiments. The Quantum Mechanical Model • Erwin Schrodinger used new theoretical calculations and experimental results to create and solve a mathematical equation describing the behavior of the electron in a hydrogen atom. • The quantum mechanical model comes from mathematical solutions to the Schrodinger equation. • It determined the allowed energies an electron can have and how likely it is to find the electron in various locations in the nucleus. Atomic Orbitals • An atomic orbital is often thought of as region of space in which there is a high probability of finding an electron. • For each principal energy level, there may be several orbitals with different shapes and at different energy levels. • These energy levels within a principal energy level make up energy sublevels. • Each energy sublevel corresponds to an orbital a different shape, which describes where the electron is likely to be found. Atomic Orbitals • The numbers and kinds of atomic orbitals depend on the • • • • • energy sublevel. The lowest principal energy level (n =1) has only one sublevel, called 1s. The second principal energy level (n=2) has two sublevels, 2s and 2p. 2p has higher energy than 2s. There are a total of four orbitals in this level. The third principal energy level (n=3) has three sublevels 3s, 3p, and 3d. There are a total of nine orbitals in this level. The fourth principal energy level (n=4) has four sublevels 4s, 4p, 4d, and 4f. There are a total of sixteen orbitals in this level. The maximum number of electrons that can occupy a principal energy level is given by the formula 2n2. Atomic Orbitals Principal Energy Level Number of Sublevels Type of Sublevel Maximum Number of Electrons n=1 1 1s (1 orbital) 2 n=2 2 2s (1 orbital), 2p (3 orbitals) 8 n=3 3 3s (1 orbital), 3p (3 orbitals), 3d (5 orbitals) 18 n=4 4 4s (1 orbital), 4p (3 orbitals), 4d (5 orbitals), 4f (7 orbitals) 32 ELECTRON ARRANGEMENT IN ATOMS Section 5.2 Electron Configurations • In an atom, electrons and the nucleus interact to make the most stab arrangement possible. • The ways in which electrons are arranged in various orbitals around the nuclei of atoms are called electron configurations. • The three rules (the aufbau principle, the Pauli exclusion principle, and Hand’s rule) tell you how to find the electron configuration of atoms. Electron Configurations • Aufbau Principle: Electrons occupy the orbitals of the • • • • • lowest energy first. The orbitals for any sublevel of a principal energy level are always of equal energy. Within a principal energy level, the s sublevel is always the lowest-energy sublevel. Pauli Exclusion Principle: An atomic orbital may have at most two electrons. To occupy the same orbital, two electrons must have opposite spins; that is, the electron spins must be paired (clockwise or counterclockwise). Hund’s Rule: Electrons occupy orbitals of the same energy in a way that makes the number of electrons with the same spin direction as large as possible. Electron Configurations • The shorthand method for showing electron configuration • • • • • • involves writing the energy level and the symbol for the sublevel. The amount of electrons in that sublevel are represented with a superscript. Examples: Hydrogen = 1s1 Helium = 1s2 Oxygen = 1s22s22p4 The sum of the superscripts equals the total number of electrons in the atom. Electron Configurations • Example Problem: Phosphorus has an atomic number of 15. Write the electron configuration for the phosphorus atom. • Solution: Atomic number = 15 = number of electrons There is a max of two electrons per orbital (s=1x2, p=3x2, d=5x2, f=7x2) 1s22s22p63s23p3 Exceptional Electron Configurations • Some actual electron configurations differ from those assigned using the aufbau principle because half-filled sublevels are not as stable as filled sublevels, but they are more stable than other configurations. • These exceptions are due to subtle electron-electron interactions in orbitals with very similar energies. • Ex: Chromium Incorrect = 1s22s22p63s23p63d44s2 (only keeping last s level full) Correct = 1s22s22p63s23p63d54s1 (keeping both d and s half full) PHYSICS AND THE QUANTUM MECHANICS MODEL Section 5.3 Light • The quantum mechanical model grew out of the study of • • • • • light, which acts in waves. The top of a wave is called the crest and the bottom is called the trough. The amplitude of a wave is a wave’s height from zero to the crest. The wavelength (λ) is the distance between the crests. The frequency (ν) is the number of wave cycles to pass a given point per unit of time. The SI unit is Hertz (Hz). The product of wavelength and frequency always equals a constant (ϲ), the speed of light. ϲ = λν Light Light • The wavelength and frequency of light are inversely • • • • • proportional to each other. For example, as the wavelength increases, the frequency decreases. Light consists of electromagnetic waves. Electromagnetic radiation includes radio waves, microwaves, infrared waves, visible light, ultraviolent waves, X-rays, and gamma rays. Sunlight consists of light with continuous range of wavelengths and frequencies. When sunlight passes through a prism, the difference frequencies separate into a spectrum of colors (ex. Rainbows). Light Atomic Spectra • When atoms absorb energy, electrons move to higher energy levels, and these electrons lose energy by emitting light when they return to lower energy levels (ex. Passing an electric current through a gas in a neon tube energizes the electrons of the atoms of the gas and causes them to emit light). • The frequencies of light emitted by an element separate into discrete lines to give the atomic emission spectrum of the element. • No two atoms have the same emission spectrum. • Atomic emission spectra are useful for identifying elements (ex. Nitrogen gas gives off a yellowishorange light). An Explanation of Atomic Spectra • The lowest possible energy of the electron is its ground • • • • state where n=1. Excitation of the electron by absorbing energy raises it to an excited state with n = 2, 3, 4, 5, 6 and so on. A quantum energy in the form of light is emitted when the electron drops back to a lower energy level. The light emitted by an electron moving from a higher to a lower energy level has a frequency directly proportional to the energy change of the electron. Therefore, each transition produces a line of a specific frequency in the spectrum. An Explanation of Atomic Spectra: Hydrogen Quantum Mechanics • Albert Einstein proposed that light could be described as • • • • quanta of energy. The quanta behave as if they were particles. Light quanta are called photons. Louis de Broglie proposed that particles of matter move in a wavelike way and that all moving objects have wavelike behavior. Classical mechanics adequately describes the motions of bodies much larger than atoms, while quantum mechanics describes the motions of subatomic particles and atoms as waves. Quantum Mechanics • Werner Heisenberg developed the Heisenberg • • • • uncertainty principle which states that it is impossible to know exactly both the velocity and the position of a particle at the same time. This, however, is not true for ordinary sized objects like cars. It is only critical in dealing with small particles like electrons. Electrons have such a small mass that striking it with a photon of light affects its motion in a way that can’t be predicted precisely. So, measuring the position of the electron changes its velocity, which makes it uncertain. Quantum Mechanics