Light. October 16, Chapter 5: Electrons in Atoms Honors Chemistry. Bohr Model

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1 Chapter 5: Electrons in Atoms Honors Chemistry Bohr Model Niels Bohr, a young Danish physicist and a student of Rutherford improved Rutherford's model. Bohr proposed that an electron is found only in specific circular paths, or orbits, around the nucleus. Each electron orbit has a fixed energy. Energy levels: the fixed energies of an electron. Quantum: The amount of energy required to move an electron from one energy level to another level. Electrons can jump from one energy level to another. The term quantum leap can be used to describe an abrupt change in energy. Light The modern quantum model grew out of the study of light. 1. Light as a wave 2. Light as a particle -Newton was the first to try to explain the behavior of light by assuming that light consists of particles.

2 Light as a Wave 1. Wavelength-shortest distance between equivalent points on a continuous wave. symbol: λ (Greek letter lambda) 2. Frequency- the number of waves that pass a point per second. symbol: ν (Greek letter nu) 3. Amplitude-wave's height from the origin to the crest or trough. 4. Speed-all EM waves travel at the speed of light. symbol: c=3.00 x 10 8 m/s in a vacuum c=3.00 x 10 8 m/s The speed of light c=λν The wavelength and frequency are inversely proportional to each other. Calculate the following: 1. The wavelength of radiation with a frequency of 1.50 x Hz. Does this radiation have a longer or shorter wavelength than red light? (2.00 x 10-5 m; longer than red) 2. The frequency of radiation with a wavelength of 5.00 x 10-8 m. In which region of the electromagnetic spectrum is this radiation? (6.00 x Hz; ultraviolet) Electromagnetic Radiation light consists of electromagnetic waves. This radiation includes radio waves, microwaves, infrared waves, visible light, ultraviolet waves, X-rays, and gamma rays. Einstein > Light as a photon > Photoelectric Effect Light as a Particle Photoelectric Effect: refers to the emission of electrons from a metal when light shines on the metal.the photoelectric effect causes electrons to be ejected from the surface of a metal when light is of high enough frequency to hit the metal's surface.

3 Light as a Particle Wave behavior of light cannot explain why heated objects give off distinct colors (specific frequencies) of light. Max Planck ( ) > studied the different wavelengths of light emitted by heated objects > conclusion: matter can gain or lose energy only in specific amounts. quantum-minimum energy that can be gained or lost by an atom > hot objects emit light in quantized amounts E=hv Planck proposed the previous relationship between a quantum of energy and the frequency of radiation. E= energy, in joules v= frequency in s -1 h= Planck's constant x J s E=hc λ Practice The yellow vapor from a sodium lamp emits 3.37 x J. What is the wavelength of this light? Physics and the Quantum Mechanical Model Wave-Particle Duality E=hv E=hc λ 3.37x J=(6.626 x Js)(3.00x 10 8 m/s 2) λ λ= 5.89 x 10-7 m or 589 nm

4 October 16, 2014 Atomic Spectra When atoms absorb energy, electrons move into higher energy levels. These electrons then lose energy by emitting light when they return to lower energy levels. Atomic emission spectrum: the frequencies of light that are emitted by an element into separate discrete lines. The fact that hydrogen atoms emit only specific frequencies of light indicated that the energy differences between the atoms' energy states were fixed. The following figure is the line-emission spectrum for hydrogen. Explanation of the Atomic Emission Spectra Bohr's model not only explained why the emission spectrum of hydrogen consists of specific frequencies of light, but it also predicted specific values of these frequencies. Ground State: When an electron has its lowest possible energy. The principal quantum number (n) is 1. *If the electron is then excited to a higher energy level, the dropping of the electron to a lower energy level creates the light emitted.

5 Quantum Mechanical Model de Broglie's Hypothesis matter has wave-like properties consequence: whole number of wavelengths must fit within the circumference of the orbit. The energy level number, n, is equal to the number of waves. Quantum Mechanical Model Heisenberg uncertainty principle: It is impossible to know exactly both the velocity and the position of a particle at the same time. We define electron energy exactly but accept that we do not know the electrons definite position. Impossible to take any measurement of an object without disturbing it! Quantum Mechanical Model Erwin Schrödinger used results to devise and solve a mathematical equation describing the behavior of the electron in a hydrogen atom. Quantum Mechanical Model *The quantum mechanical model determines the allowed energies of an electron and how likely it is to find the electron in various locations around the nucleus. Probability of finding a hydrogen electron. We can apply to other elements.

6 Orbit vs. Orbital Orbit: defined path of an electron (Bohr) Orbital: defined area of space for finding an electron. (Schrodinger) Types of Orbitals The most probable area to find these electrons take on a shape. So far, we have 4 shapes. > s, p, d, f. No more than 2 electrons assigned to an orbital. > One spins clockwise, one spins counterclockwise.

7 Atomic Orbitals and Quantum Numbers Quantum numbers specify the properties of atomic orbitals and the properties of electrons in orbitals. This first three quantum numbers result from the Schrödinger equation. Quantum Number Symbol n l m l m s Definition principle quantum number angular momentum quantum number (shape of the orbital) magnetic quantum number (orientation) spin quantum number Principal Quantum Number (n) Indicates the main energy level occupied by the electron. n= 1, 2, 3 and so on. As n increases, the electron's energy and its average distance from the nucleus increases. *The total number of orbitals that exist in a given shell Angular Momentum Quantum Number (l) Indicates the shape of the orbital. The number of orbital shapes possible is equal to n. l=n-1 L value 0 s 1 p 2 d 3 f Letter/Shape Ex: If n=2; L has two sublevels, the s and p orbitals because l=n-1; l=0 and 1 How many sublevels would n=3 have?

8 Magnetic Quantum Number (ml) Indicates the orientation of an orbital around the nucleus. Values of m are whole numbers; 0 from L to -L m=-l l Spin Quantum Number (ms) Only two possible values (+1/2 and -1/2) which indicate the two fundamental spin states of an electron in an orbital. A single orbital can then hold how many electrons? Because an s orbital is spherical and is centered around the nucleus, it has only one possible orientation. How many orientations are present in the following orbitals? Tying all Quantum Numbers Together We can combine all four quantum numbers together to give us p orbitals d orbitals 1 atomic orbital contains 2 electrons. Depending on the subshell, there may be different number of atomic orbitals present. The combination of the quantum numbers will tell us whether we are talking about an entire subshell or one atomic orbital. *This may seem confusing until we do an example f orbitals Tying all Quantum Numbers Together Table of Allowed Quantum Numbers n=1, L= 0, ml=0, ms= +1/2, -1/2 This is one atomic orbital n l m ms 2 If I asked you to write all of the allowed quantum number combinations for n=3, this would be all quantum numbers for the n=3 subshell.

9 Definition Electron Configuration Introduction 1. Aufbau Principle Electrons occupy the orbitals of lowest energy first. October 16, 2014 The ways in which electrons are arranged in various orbitals around the nuclei of atoms. Change proceeds toward the lowest possible energy. 3 Rules: These three rules tell you how to find the electron configurations of atoms. 1. Aufbau principle 2. Pauli Exclusion Principle 3. Hund's Rule 2. Pauli Exclusion Principle an atomic orbital may describe at most two electrons. *To occupy the same orbital, two electrons must have opposite spins. 3. Hund's Rule electrons occupy orbitals of the same energy in a way that makes the number or electrons with the same spin direction as large as possible.

10 Orbital Notation vs. Electron-Configuration Notation Orbital Notation: an unoccupied orbital is represented by a line,, with the orbital's name written underneath the line. An orbital containing one electron is represented as. A orbital containing two electrons is represented as. Electron-Configuration Notation: Eliminates the lines and arrows. Instead, the number of electrons in a sublevel is shown by adding a superscript to the sublevel. What element is represented by the following orbital diagram? How many unpaired electrons are present? 1s 2 2s 2 2p 6 3s 1 Ex: Hydrogen is represented by 1s 1 Example: H, He, Li, Be, B Sample Problem The electron configuration of boron is 1s 2 2s 2 2p 1. How many electrons are resent in an atom of boron? What is the atomic number for boron? Write the orbital notation for boron. Steps for Writing Electron Configurations 1. Locate the element on the periodic table. 2. Start by filling in the electrons from the lowest possible energy state first. (Noble Gas Configuration ONLY after some practice!) 3. Continue filling higher in energy until all electrons are used. 4. Do not forget to obey the three rules of Aufbau, Hund and Pauli. How many unpaired electrons are present? Noble Gas Shortcut Examples (Cd) 1. Find the noble gas (group 18 on the periodic table) with an atomic number less than the element...kr 2. Put the noble gas in brackets...[kr] 3. The noble gas filled the p sublevel with n=period number Follow the periodic table/diagonal rule and continue the notation from the next s-sublevel using the remaining electrons...[kr]5s 2 4d 10 H He Li N Fe U Electron Configuration Practice

11 Nobel Gas Shorthand When you are writing electron configurations for elements that have large atomic numbers, you may use the nobel gas configuration shortcut. You use the most previous noble gas in brackets [He], and then finish the electron configuration the normal way. Ions If you have an element that has a positive or negative charge, you will add or take away electrons based on the charge. You MUST take electrons away from the highest energy level (n) first!!!!! Example: Cl - : You must add an electron W 2+ : Take 2 electrons away from the outermost energy level! Exceptional Electron Configurations Write what you would expect the electron configuration for copper (Cu) and chromium (Cr) to be. 3 Types of Notation Cu Cr *Some actual electron configurations differ from those assigned using the aufbau principle because half-filled sublevels are not as stable as filled sublevels.

12 Practice Different Notations Practice Different Notations