Quantum Mechanical Model of the Atom PDF

Quantum Mechanical Model of the Atom Quarter 2: General Chemistry 1  The Beginnings of Quantum Mechanics Until the beginning of the twentieth century it was believed that all physical phenomena were deterministic. Work done at that time by many famous physicists discovered th...

Quantum Mechanical Model of the Atom Quarter 2: General Chemistry 1  The Beginnings of Quantum Mechanics Until the beginning of the twentieth century it was believed that all physical phenomena were deterministic. Work done at that time by many famous physicists discovered that for sub-atomic particles, the present condition does not determine the future condition. Albert Einstein, Neils Bohr, Louis de Broglie, Max Planck, Werner Heisenberg, P. A. M. Dirac, and Erwin Schrödinger The Beginnings of Quantum Mechanics Quantum mechanics forms the foundation of chemistry Explaining the periodic table The behavior of the elements in chemical bonding Provides the practical basis for lasers, computers, and countless other applications The Behavior of the Very Small Electrons are incredibly small. A single speck of dust has more electrons than the number of people who have ever lived on Earth. Electron behavior determines much of the behavior of atoms. Directly observing electrons in the atom is impossible; the electron is so small that observing it changes its behavior. Even shining a light on the electron would affect it. A Theory That Explains Electron Behavior The quantum-mechanical model explains the manner in which electrons exist and behave in atoms. It helps us understand and predict the properties of atoms that are directly related to the behavior of the electrons: Why some elements are metals and others are nonmetals Why some elements gain one electron when forming an anion, whereas others gain two Why some elements are very reactive, while others are practically inert Why in other periodic patterns we see in the properties of the elements Engage: What causes the colors in fireworks displays? What do you think give the colors in the fireworks? What causes the colors in neon lights? The Dual Nature of Matter A Particle is an object which has distinct chemical and physical properties such as volume or mass A Wave is a disturbance that travels from one location to another. The Wave Nature of Light Light: a form of electromagnetic radiation Composed of perpendicular oscillating waves, one for the electric field and one for the magnetic field An electric field is a region where an electrically charged particle experiences a force. A magnetic field is a region where a magnetized particle experiences a force. All electromagnetic waves move through space at the same, constant speed. 3.00 × 108 m/s = the speed of light Electromagnetic Radiation © 2014 Pearson Education, Inc. Speed of Energy Transmission The Characteristics of a Wave Parts of a wave: amplitude, crest, trough Wavelength (λ) – distance from crest to crest or trough to trough Frequency (f) – how many waves pass a point during a given unit of time the number of waves = the number of cycles. Units are hertz (Hz) or cycles/s = s−1 Characterizing Waves The amplitude is the height of the wave. The distance from node to crest or node to trough The amplitude is a measure of light intensity—the larger the amplitude, the brighter the light. The wavelength (l) is a measure of the distance covered by the wave. The distance from one crest to the next The distance from one trough to the next, or the distance between alternate nodes Wave Characteristics Characterizing Waves The frequency (n) is the number of waves that pass a point in a given period of time. The number of waves = the number of cycles. Units are hertz (Hz) or cycles/s = s−1 (1 Hz = 1 s−1). The total energy is proportional to the amplitude of the waves and the frequency. The larger the amplitude, the more force it has. The more frequently the waves strike, the more total force there is. Amplitude and Wavelength © 2014 Pearson Education, Inc. The Relationship Between Wavelength and Frequency For waves traveling at the same speed, the shorter the wavelength, the more frequently they pass. This means that the wavelength and frequency of electromagnetic waves are inversely proportional. Because the speed of light is constant, if we know wavelength we can find the frequency, and vice versa. Wave Equations of Light Frequency is inversely related to the wavelength by the speed of light. c = ln where l = wavelength, n = frequency, and c = speed of light = 3 x 108 m/s Wave Equations of Light  The wavelength of the wave multiplied by the frequency of the wave corresponds to the speed, μ, of the wave. In an equation form, μ = ln Theories of Quantum Mechanics  Planck’s Quantum Theory Planck made a radical proposal to explain the experimental results of the blackbody radiation. A blackbody is a material that absorbs all radiation that falls on it and is therefore a perfect absorber. It then emits thermal radiation in a continuous spectrum according to its temperature. (Planck’s Equation) → E=hv THE PARTICLE-WAVE DUALITY OF LIGHT Light also has properties of particles. These particles have mass and velocity. A particle of light is called a photon. E=hv Where, v is the frequency And h is Planck’s constant: 6.626 x 10-34 J.s THE DUAL NATURE OF THE ELECTRON: DE BROGLIE’S EQUATION Louis de Broglie made a bold proposition based on Planck’s and Einstein’s concepts. He reasoned that if light could have particle-like properties, then particles like electrons could also have wavelike properties. Diffraction When traveling waves encounter an obstacle or opening in a barrier that is about the same size as the wavelength, they bend around it; this is called diffraction. Traveling particles do not diffract. The diffraction of light through two slits separated by a distance comparable to the wavelength results in an interference pattern of the diffracted waves. An interference pattern is a characteristic of all light waves. Diffraction Interference The interaction between waves is called interference. Constructive interference: when waves interact so that they add to make a larger wave, it is called in phase. Destructive interference: when waves interact so they cancel each other it is called out of phase. Interference Two-Slit Interference  h l= mv Wave and Particle To relate the properties of waves and particles, use De Broglie’s equation: l = h/mv Where; l = wavelength, h = Planck’s constant; m = mass in kg and v = velocity in m/s CALCULATING THE DE BROGLIE’s WAVELENGTH What is the wavelength of an electron moving at 5.31 x 106 m/sec? Given: mass of the electron = 9.11 x 10-31 kg h = 6.626 x 10-34 J·s Solution: de Broglie's equation is λ = h/mv λ = 6.626 x 10-34 J·s/ 9.11 x 10-31 kg x 5.31 x 106 m/s λ = 6.626 x 10-34 J·s/4.84 x 10-24 kg·m/s λ = 1.37 x 10-10 m  Exercises An electron of mass at 9.11 x 10-31 kg moves at nearly the speed of light. Using a velocity of 3.00 x 108 m/s, calculate the wavelength of the electron. Given: m = 9.11 x 10-31 kg h = 6.626 x 10-34 J·s c = 3.00 x 108 m/s Solution: de Broglie's equation is λ = h/mv λ = 6.626 x 10-34 J·s/ 9.11 x 10-31 kg x 3.00 x 108 m/s λ = 6.626 x 10-34 J·s/2.733 x 10-22 kg·m/s λ = 2.42 x 10-12 m  Study of Light Visible light comprises only a small fraction of all the wavelengths of light, called the electromagnetic spectrum. Shorter wavelength (high-frequency) light has higher energy. Color The color of light is determined by its wavelength or frequency. White light is a mixture of all the colors of visible light. A spectrum Red Orange Yellow Green Blue Indigo Violet When an object absorbs some of the wavelengths of white light and reflects others, it appears colored; the observed color is predominantly the colors reflected. Spectrum of Colors When atoms or molecules absorb energy, that energy is often released as light energy, such as fireworks, neon lights, etc. When that emitted light is passed through a prism, a pattern of particular wavelengths of light is seen that is unique to that type of atom or molecule – the pattern is called an emission spectrum. Can be used to identify the material Flame tests Splitting Light Identifying Elements with Flame Tests Na K Li Ba © 2014 Pearson Education, Inc. Spectrums The lines on the emission or absorption spectrums of an element are produced when the electrons in that atom change energy levels (orbitals). Sources of Spectrums Emission Spectra © 2014 Pearson Education, Inc. Examples of Spectra The Photoelectric Effect It was observed that many metals emit electrons when a light shines on their surface. This is called the photoelectric effect. Classic wave theory attributed this effect to the light energy being transferred to the electron. According to this theory, if the wavelength of light is made shorter, or the light wave’s intensity made brighter, more electrons should be ejected. Remember that the energy of a wave is directly proportional to its amplitude and its frequency. This idea predicts if a dim light were used there would be a lag time before electrons were emitted. To give the electrons time to absorb enough energy The Photoelectric Effect © 2014 Pearson Education, Inc. The Photoelectric Effect: The Problem Experimental observations indicate the following: A minimum frequency was needed before electrons would be emitted regardless of the intensity is called the threshold frequency. High-frequency light from a dim source caused electron emission without any lag time. Einstein’s Explanation Einstein proposed that the light energy was delivered to the atoms in packets, called quanta or photons. The energy of a photon of light is directly proportional to its frequency. Inversely proportional to its wavelength The proportionality constant is called Planck’s Constant, (h), and has the value of 6.626 × 10−34 J ∙ s. Ejected Electrons One photon at the threshold frequency gives the electron just enough energy for it to escape the atom. Binding energy, f / Work Function (W) When irradiated with a shorter wavelength photon, the electron absorbs more energy than is necessary to escape. This excess energy becomes kinetic energy of the ejected electron. Kinetic Energy = Ephoton – Ebinding KE = hn − f A Quantum of Energy The smallest amount of energy that can be emitted or absorbed in the form of electromagnetic radiation is known as quantum. A packet of energy required to move an electron from its present energy level to a higher one.  Planck’s Hypothesis (Quantum Theory) - energy is given off in little packets, or quanta, instead of continuously. Different atoms and molecules can emit or absorb energy in discrete quantities only.  Energy How much energy is emitted by a photon of light can be calculated by E = hn where E = energy of the photon, h = Planck’s constant = 6.626 x 10-34 J s n = frequency Typical Units n = waves per second (s-1) l = meters, (m) (note: 1 m = 1 x 109 nm), E = Joules (J), h, Planck’s constant = Joules x Seconds, (J s) m = kilograms v = meters per second, m/s Exercises: Exercises: ATOMIC MODEL The Bohr Model of the Atom Neils Bohr (1885–1962) The nuclear model of the atom does not explain what structural changes occur when the atom gains or loses energy. Bohr developed a model of the atom to explain how the structure of the atom changes when it undergoes energy transitions. Bohr’s major idea was that the energy of the atom was quantized, and that the amount of energy in the atom was related to the electron’s position in the atom. Quantized means that the atom could only have very specific amounts of energy. Bohr’s Planetary Model Bohr’s Model The electrons travel in orbits that are at a fixed distance from the nucleus. Stationary states Therefore, the energy of the electron was proportional to the distance the orbit was from the nucleus. Electrons emit radiation when they “jump” from an orbit with higher energy down to an orbit with lower energy. The emitted radiation was a photon of light. The distance between the orbits determined the energy of the photon of light produced. Bohr Model of Atoms © 2014 Pearson Education, Inc. However; The Bohr model violates Heisenberg’s Uncertainty Principle. Electrons do not go around the nucleus in well-defined orbits. Otherwise, we will be able to determine the exact position and momentum of the electron in the atom at the same time. A better model is needed to fully describe the atom. Quantum Mechanical Model or Wave model Describes the 3Dimensional position of the electron in a probabilistic manner according to a mathematical function called a wavefunction (orbitals). Small, dense, positively charged nucleus surrounded by electron clouds of probability. Does not define an exact path an electron takes around the nucleus. Electron cloud – the volume in which the electron is found 90% of the time Quantum Mechanical Model Solutions to the Wave Function, Y Calculations show that the size, shape, and orientation in space of an orbital are determined to be three integer terms in the wave function. Added to quantize the energy of the electron. These integers are called quantum numbers. Principal quantum number, n Angular momentum quantum number, l Magnetic quantum number, ml Spin quantum number, s Quantum Numbers Used to describe an electron’s behavior or likely location There are four with variables: n, l, m, & s Principal Quantum Number (n) Corresponds to the energy levels 1 through n. However, we will only deal with 1-7. Average distance from the nucleus increases with increasing principal quantum number, therefore n designates the size of the electron cloud Maximum # of electrons in each energy level is calculated by 2n2 where n = the energy level (1-7). Energy Sublevels (l) 2nd quantum number The number of sublevels equals the value of the principal quantum number (n) for that level. Sublevels are named in the following order - s, p, d, f. The l number designates the shape of the electron cloud. S sublevel – spherical shape P sublevel - dumbbell shaped D sublevel clover-leaf shaped F sublevel – irregularly shaped Orbitals (m) 3rd quantum number (m) The space occupied by a pair of electrons in a certain sublevel. Sublevel s - 1 orbital p - 3 orbitals d - 5 orbitals f - 7 orbitals Each orbital can hold two electrons. m represents the orientation in space of the orbitals (x axis, y axis, z axis) Animation Spin (s) 4th quantum number Distinguishes between the electrons in the same orbital. describes the electrons spin as either clockwise or counter- clockwise Shape of the electron cloud Size (diameter) is related to n, the principle quantum number. The larger n, the larger the electron cloud. Shape is given by the sublevel, (l). The direction in space is given by the orbital,(m).