* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download The Quantum Mechanical Model of the Atom
Interpretations of quantum mechanics wikipedia , lookup
Franck–Condon principle wikipedia , lookup
Quantum group wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Quantum key distribution wikipedia , lookup
Quantum teleportation wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Probability amplitude wikipedia , lookup
EPR paradox wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Chemical bond wikipedia , lookup
Canonical quantization wikipedia , lookup
History of quantum field theory wikipedia , lookup
Quantum state wikipedia , lookup
Matter wave wikipedia , lookup
Hidden variable theory wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Rutherford backscattering spectrometry wikipedia , lookup
Wave–particle duality wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Particle in a box wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Molecular orbital wikipedia , lookup
Tight binding wikipedia , lookup
Atomic theory wikipedia , lookup
Atomic orbital wikipedia , lookup
Chapter 2.2 Structure of the atom The Quantum Mechanical Model collide, some of the kinetic energy from one atom is transferred to the other atom. The electron of the second hydrogen atom absorbs this energy Figure 3.6 The electromagnetic spectrum and its properties and is excited to a higher energy level. When the electron of a hydrogen atom that has been excited to the Thethird visible portion of falls the electromagnetic spectrum continuous energy level to the second energy level,isitcalled emits alight of certain spectrum, because the component colours are indistinct. They appear energy. Specifically, an electron that makes a transition from the third “smeared” together into a continuum of colour. tored nineteenthenergy level to the second energy level emitsAccording a photon of light with century physics, part of the energy emitted by electrons should be a wavelength of 656 nm. Because line spectra result when atoms in an observable a continuous spectrum. Thistoisa not, however, the case. excited as state emit photons as they fall lower energy level, these Instead, when atoms absorb energy (for example, when they are exposed spectra are also called emission spectra. to an electric you pattern of that discrete (distinct), for the Figurecurrent), 3.9 shows theobserve energy atransitions are responsible coloured lines separated by spaces of varying length.Notice See Figure 3.7. coloured lines in hydrogen’s emission spectrum. the use ofYou the can symbol also observe this line spectrum for hydrogen, and for other atoms, in n to designate the allowed energy levels for the hydrogen atom: Investigation n = 1, n = 3-A. 2, and so on. This symbol, n, represents a positive integer (such number. You will learn more about 400 as 1, 2, or 3), and 500 is called a quantum 600 750 nm the significance of quantum numbers in section 3.2. The Quantum Mechanical Model of the Atom Following Bohr’s Atomic Model, atoms have specific energy levels (or electrons orbits). When excited, electrons change energy level by emitting or absorbing a specific quantity of energy called quanta. 400 500 600 750 nm Figure 3.7 The discrete, coloured lines of this spectrum are characteristic of hydrogen atoms. No other atoms display this pattern of coloured lines. n=6 n=5 n=4 n=3 Chapter 3 Atoms, Electrons, and Periodic Trends • MHR 123 e- n=2 nn=3 =1 n=2 energy n=2 nn=4 =3 n=4 n=5 n=5 n=6 n=6 A Note: Orbits are not drawn to scale. n=1 B Note: In its unexcited state, hydrogen‘s electron is in the energy level closest to the nucleus: n = 1. This is the lowest-possible energy level, representing a state of greatest stability for the hydrogen atom. hydrogen atom. suggested As you can seethere in Figure mercury more spectral lines, however, that were 3.12, smaller energyhas differences lines hydrogen Thewords, same isscientists true for other many-electron atoms withinthan energy levels.does. In other hypothesized that there ar Observations likeeach theseenergy forcedlevel. BohrEach and other scientists to reconsider sublevels within of these sublevels has its ownthe nature energyelectrons levels. largeaspaces between the individual colours slightly energy.Thethan A mercury (Hg) atom hasofdifferent more hydrogen atom and has more suggested that there are energy differences between individual energy spectral lines than hydrogen does. Hg levels, as stated in Bohr’s model. The smaller spaces between coloured lines, that550 there were differences 400 however, 450 suggested 500 600 smaller 650energy700 750 nm within energy levels. In other words, scientists hypothesized that there ar H Hydrogen spectrum sublevels within each energy level. Each of these sublevels has its own slightly different energy. 400 450 500 550 600 650 700 750 nm How Bohr’s Atomic Model Explains the Spectrum Mercury spectrum The emission spectrum for mercury shows that it has more spectral lines Hg the emission spectrum for hydrogen. than Figure 3.12 400 450 500 550 600 650 700 750 nm It was fairly straightforward to modify Bohr’s model to include the idea H The large spaces of between individual suggested that there energy the sublevels for colors the hydrogen spectrum andare for energy atoms or ions with 400 one electron. 450 500 was550 600 700 however. 750 nm The only There a moreasfundamental problem, differences between individual energy levels, stated in 650 Bohr’s model. Figure 3.12 model still could not explain spectrashows produced by more many-electron The emission spectrumthe for mercury that it has spectral lines than the emission spectrum for hydrogen. atoms. Therefore, a simple modification of Bohr’s atomic model was not The smaller spaces between colored lines, however, suggested that there were enough. The many-electron problem called for a new model to explain smaller energy differences within energy levels. It was fairly straightforward modify Bohr’s model to include theanother idea spectra of all types of atoms.to However, this was not possible until of energy sublevels formatter the hydrogen spectrum and for atoms or ions with important property of was discovered. only one electron. There was a more fundamental problem, however. The In other words model stillsub-levels couldof not explain theenergy spectralevel” produced by many-electron “there are within each . The Discovery Matter Waves atoms. Therefore, a simple modification of Bohr’s atomic model was not Each of these sub-levels itsearly own energy Byhas the 1920s, it was standard knowledge that energy had matter-like enough. The many-electron problem called for a new model to explain properties. In 1924, a young physics student named Louis de Broglie spectra of all types of atoms. However, this was not possible until another The Discovery of Matter Waves In 1924, the physics student Louis de Broglie stated an idea: “What if matter has wave-like properties?” He developed an equation to calculate the wavelength (λ) associated with any object (large, small, or microscopic). E.g. A baseball with a mass of 142 g and moving with a speed of 25.0 m/s has a wavelength of 2 × 10−34 m. Objects that you can see and interact with, such as a baseball, have wavelengths so small that they do not have any significant observable effect on the object’s motion. For microscopic objects, such as electrons, the effect of wavelength on motion becomes very significant. E.g. An electron moving at a speed of 5.9 × 106 m/s has a wavelength of 1 × 10−10 m. The size of this wavelength is greater than the size of the hydrogen atom to which it belongs. The Quantum Mechanical Model of the Atom In 1926, an Austrian physicist, Erwin Schrödinger, used mathematics and statistics to combine de Broglie’s idea of matter waves and Einstein’s idea of quantized energy particles (photons). This resulted in the birth of Quantum Mechanics. This is a branch of physics that uses mathematical equations to describe the wave properties of sub-microscopic particles such as electrons, atoms, and molecules. Schrödinger proposed a new atomic model: the quantum mechanical model of the atom. The model of the atom in 1927. The fuzzy, spherical Figure 3.13 Schrödinger and the orbital Schrödinger’s quantum mechanical model describes atoms as having certain allowed quantities of energy because of the wave-like properties of their electrons. The volume surrounding the nucleus is indistinct because of a principle called “the uncertainty principle”. The physicist Werner Heisenberg proposed, using mathematics that it is impossible to know precisely both the position and the momentum of an object. (recall: An object’s momentum is given by its mass multiplied by its velocity). E.g. According to the uncertainty principle, if you can know an electron’s precise path around the nucleus (orbit), you cannot know with certainty its velocity. Similarly, if you know its precise velocity, you cannot know with certainty its position. Schrödinger used an equation called a wave equation to define the orbital as the “probability of finding an atom’s electrons at a particular point within the atom”. Chemists call these wave functions orbitals The model of the atom in 1927. The fuzzy, spherical Figure 3.13 A level of probability is usually expressed as a percentage. Therefore, Schrödinger and the3.14B orbital the contour line in Figure defines an area that represents 95 percent of the probability graph. This two-dimensional shape is given three Each orbital has its own associated energy, and each represents information about where, dimensions in Figure 3.14C. What this means is that, at any time, there inside the atom, the electrons would spend most of their time. However, orbitals indicate is there a 95 percent chance ofoffinding the electron within the volume defined where is a high probability finding electrons by the spherical contour. A B + C + + Fig.3.14 A: probability of finding an probability electron at any point in when theenergy electron is at in thethe lowest Figure Electron density graphs forspace the lowest level hydrogen energy level (n = 1) of a hydrogen atom. Where the density of the dots is greater, there is a atom. These diagrams represent the probability of finding an electron at any point in this higher probability of finding the electron. energyFig. level. B defines an area that represents 95 percent of the probability graph. This two-dimensional shape is given three dimensions in Fig. C Quantum Numbers and Orbitals Figure 3.14 showed electron-density probabilities for the lowest energy level of the hydrogen atom. This is the most stable energy state for hydrogen, and is called the ground state. The quantum number, n, for a of the probability graph. This two-dimensional shape is given three Quantum Numbers and Orbitals dimensions in Figure 3.14C. What this means is that, at any time, there is a lowest 95 percent ofhydrogen findingatom the electron theis volume The energy chance level of the is the mostwithin stable and called the defined ground state. by the spherical contour. The quantum number, n, for a hydrogen atom in its ground state is 1. A B + C + + Orb When n=1 in the atom, its electron is associated with an orbital that has a characteristic energy scienti Figure 3.14In an Electron for with the lowest energy level hydrogen and shape. exciteddensity state, theprobability electron is graphs associated a different orbital withinitsthe own Orbitals have a variety of differ characteristic energy and shape. the probability of finding an electron atom. These diagrams represent at any point in this quantu scientists use three quantum numb The figure below compares the sizes of hydrogen’s orbitals when the atom is in its ground state n = 1 energy level. (n=1) and when it is in an excited state(n=2 quantum number, n, describes an o quantu n = 1 and n=3). quantum number, l, describes an o l , des ml , describes an orbital’s m orientatio Quantum Numbers and Orbitals numbers are described further belo numbe Figure 3.14 showed electron-density probabilities for the lowest energy afterward summarizes this informa afterwa level of the hydrogen atom. This is the most stable for number, m aboutenergy a fourthstate quantum n=2 n=1 n=2 n=3 hydrogen, and is called the ground state. The number, n, for a about a electron inside an orbital.) n =quantum 2 n=1 n=2 Orbitals have a variety of different possible shapes. Therefore, scientists use three quantum numbers to describe an atomic orbital. One quantum number, n, describes an orbital’s energy level and size. A second quantum number, l, describes an orbital’s shape. A third quantum number, ml , describes an orbital’s orientation in space. These three quantum numbers are described further below. The Concept Organizer that follows afterward summarizes this information. (In section 3.3, you will learn about a fourth quantum number, ms, which is used to describe the electron inside an orbital.) The First Quantum Number: Describing Orbital Energy Level and Size Quantum Numbers and Orbitals Non excited orbitals have different possible shapes. Three quantum numbers are used to describe an atomic orbital. 1. One quantum number, n, describes an orbital’s energy level and size. 2. A second quantum number describes the orbital’s shape. 3. A third quantum number describes the orbital’s orientation in space. The First Quantum Number: Describing Orbital Energy Level and Size The principal quantum number (n) is a positive number that specifies the energy level of an orbital and its size. The value of n, therefore, may be 1, 2, 3.... A higher value for n indicates a higher and larger energy level, with a higher probability of finding an electron farther from the nucleus. The maximum number of electrons that is possible in any energy level is 2n2. value of “n” maximum number of ein the energy level 1 2 2 8 3 18 The Second Quantum Number: Describing Orbital Shape The second quantum number, or angular quantum number (l) describes the orbital’s shape and is a positive integer that ranges from 0 to (n−1). The number of possible values for l in a given energy level is the same as the value of n. e.g. if n = 2, then there are only two types of orbital shapes at this energy level. value of “n” values of “l” 1 0 2 0 or 1 3 0, 1 or 2 4 0,1,2 or 3 The Second Quantum Number: Describing Orbital Shape Each value for l is given a letter: s, p, d, or f • • • • The l=0 orbital has the letter s The l=1 orbital has the letter p The l=2 orbital has the letter d The l=3 orbital has the letter f To identify an energy type of orbital, you combine the value of n with the letter of the orbital shape. e.g. The orbital with n=3 and l=0 is called the 3s orbital. The orbital with n=2 and l=1 is the 2p orbital The Third Quantum Number: Describing Orbital Orientation The magnetic quantum number (m) is an integer with values ranging from -l to +l, including 0. This quantum number indicates the orientation of the orbital in the space. The value of m is limited by the value of l. If l=0, m can be only 0. e.g. If l=1, m may have one of three values: -1, 0, or +1. If l=2, m may have one of five values: -2,-1, 0, +1 or +2. In other words, for a given value of n, there is one orbital s (l=0) and three orbitals of p (l=1). Each of these p orbitals has the same shape and energy, but a different orientation around the nucleus. value of “n” values of “l” values of “m” 1 0 0 2 0 0 1 -1, 0, +1 2 -2,-1, 0, +1, +2 Quantum Numbers The total number of possible orbitals for any energy level n is given by n2 . For example, if n = 2, it has a total of 4 (22) orbitals (one s orbital and three p orbitals) n 1 Quantum number l m 0 0 type s Orbital name 1s quantity 1 2 0 1 0 -1, 0, +1 s p 2s 2p 1 3 3 0 1 2 0 -1, 0, +1 -2,-1, 0, +1, +2 s p d 3s 3p 3d 1 3 5 4 0 1 2 3 0 -1, 0, +1 -2,-1, 0, +1, +2 -3,-2,-1,0,+1,+2,+3 s p d f 4s 4p 4d 4f 1 3 5 7 Sample Problems Determining Quantum Numbers If n=3, what are the allowed values for l and m? What is the total number of orbitals in this energy level? The allowed values for l range from 0 to (n−1). The allowed values for m are integers ranging from −l to +l including 0. Since each orbital has a single m value, the total number of values for m gives the number of orbitals. • To find l from n: If n=3, l may be either 0, 1, or 2. • To find ml from l: If l=0, m=0 If l=1,m maybe -1,0,+1 If l=2, m maybe -2,-1,0,+1,+2 • Since there are a total of 9 possible values for m , there are 9 orbitals when n=3 (32). What are the possible values for m if n=5 and l=1? What kind of orbital is described by these quantum numbers? How many orbitals can be described by these quantum numbers? Determine the type of orbital by combining the value for n with the letter used to identify l. You can find possible values for m from l, and the total of the m values gives the number of orbitals. • • • To name the type of orbital: l=1, which describes a p orbital Since n=5, the quantum numbers represent a 5p orbital. To find m from l: If l=1, m maybe -1, 0, +1 Therefore, there are 3 possible 5p orbitals. measured, and trajectories that can be photographed. They exist in the physical universe. Orbitals are mathematical descriptions electrons. They do not An orbital is •associated with a size, a shape and anoforientation around thehave nucleus. measurable physical properties such as or temperature. Theya exist Together, the size, shape and position represent themass probability of finding specific in the imagination. Shapes of Orbitals electron around the nucleus of an atom. The figure shows the probability shapes associated with the s, p, and d orbitals s orbitals n=1 !=0 p orbitals z z z y y n=2 !=1 x m =-1 d orbitals z y y x x n=3 !=2 m =-1 y n=2 !=1 x m =0 z z n=3 !=2 m =-2 n=3 !=0 n=2 !=0 n=3 !=2 m =0 n=2 !=1 x m =+1 z z y y x x n=3 !=2 m =+1 y n=3 !=2 m =+2 x Shapes of the s, p, and d orbitals. Orbitals in the p and d sublevels are oriented along or between perpendicular x, y, and z axes. Figure 3.16 Notice that the overall shape of an atom is a combination of all its orbitals. Thus, the overall shape of an atom is spherical.