QUANTUM THEORY & ATOMIC STRUCTURE. GENERAL CHEMISTRY by Dr. Istadi

Transcription

1 QUANTUM THEORY & ATOMIC STRUCTURE GENERAL CHEMISTRY by Dr. Istadi 1

2 THE NATURE OF LIGHT Visible light is one type of electromagnetic radiation ( radiation (electromagnetic The electromagnetic radiation has the wave properties: Frequency (ν): the number of cycles the wave undergoes per second ==> 1/second Hz Wavelength (λ): the distance between any point on a wave and the corresponding point on the next crest of the wave (the distance the wave travels during one cycle) ==> m, nm, ( m Å (

3 Speed of light (c): 3 x 10 8 m/s ==> c = v x λ where c is constant That's mean, radiation with a high frequency has a short wavelength, and vice versa Another characteristic of a wave is: AMPLITUDE Amplitude: the height of the crest of each wave or intensity of the wave/radiation The two waves shown have the same wavelength (color) but different amplitudes, and therefore different brightnesses ( intensities ) 3

4 The Electromagnetic Spectrum Visible light represents a small portion of the continuum of radiant energy, known as electromagnetic spectrum All the waves in the spectrum travel at the same speed through a vacuum but differ in frequency and therefore wavelength Wavelength of visible light as different colors: from red (λ=750 nm) to ( nm violet (λ=400 Light of single wavelength is called MONOCHROMATIC Light of many wavelength is called POLYCHROMATIC 4

5 Distinction Between Energy and Matter In contrast, a particle does not undergo refraction when passing a boundary when light wave passes from air to water, the speed of the wave changes ==> refraction After strikes the boundary, the light continues at a different angle, therefore change in speed and direction The new angle depends on the materials on either side of the boundary and the wavelength of the light White light is dispersed into its component colorsm when pass through a prism, because each incoming wavelength is refracted at a slightly different angle. 5

6 If waves of light pass through two adjacent slits, the emerging circular waves interact with each other through the process of interference. If the crests of the waves coincide (in phase), they interfere constructively and the amplitudes add together. If the crests coincide with throughs (out of phase), they interfere destructively and the amplitudes cancel. the result is a diffraction pattern of brighter and darker regions 6

7 The Particle Nature of Light 1.Blackbody Radiation 2.The Photoelectric effect 3.Atomic Spectra 7

8 Blackbody Radiation ( glow When a coal is heated to 1000 K ==> emit visible light (red At 1500 K, the light is brighter and more orange, like that from an ( listrik electric heating coil (elemen pemanas These changes in intensity and wavelength of emitted light as an object is heated are characteristic of blackbody radiation. In 1900, Max Planck ==> hot or glowing object could emit or absorb only certain quantities of energy: E = nhv E: energy of radiation (J); v : frequency (s -1 ); n : positive integer of a quantum number; h : proportionality constant (Planck's constant in ( J.s h = x J.s = x J.s 8

9 Quantum Energy If an atom itself can emit only certain quantities of energy ==> the atom itself can have only certain quantities of energy Thus, the energy of an atom is quantized Each change in the atom's energy results from the gain or loss of one or more packet (amount) of energy. ( hv Each energy packet is called a quantum (= An atom changes its energy state by emiting (or absorbing) one or more quanta, and the energy of the emitted (or absorbed) radiation is equal to the difference in the atom's energy states: ΔE atom = E emitted (or absorbed) radiation = Δnhv The atom can change its energy only by integer multiples of hv ==> the smallest changes occurs when an atom in a given energy state changes to an adjacent states when Δn=1 ΔE = hv 9

10 Photoelectric Effect and Photon Theory of Light When monochromatical light of high enough frequency strikes the metal plate, electrons are freed from the plate and travel to the positive electrode, creating a current Plank's idea of quantized energy ==> Einstein: light itself is particulate, that is quantized into small bundles of electromagnetic energy ==> PHOTONS Planck ==> each atom changes its energyu whenever it absorbs or emits one photon, one particle of light, whose energy is fixed by its frequency: E photon = hv = ΔE atom 10

11 How Einstein's Photon Theory Explains the Photoelectric Effect? According to the photon theory, a beam of light consists of an enormous number of photons. Light intensity is related to the number of photons striking the surface per unit time, but not to their energy. Therefore, a photon of a certain minimum energy must be absorbed for an electron to be freed. Since energy depends on frequency (hv), the theory predicts a threshold frequency. An electron can not save up energy from several photons below the minimum energy until it has enough to break free. Rather, one electron breaks free the moment it absorbs one photon of enough energy. The current is weaker in dim light than in bright light because fewer photons of enough energy are present, so fewer electrons break free per unit time. But some current flows the moment photons reach the metal plate 11

12 Examples of Energy Radiation A cook uses a microwave oven to heat a metal. The wavelength of the radiation is 1.20 cm. What is energy of one photon of this microwave radiation? Solution: E = hv = hc/λ ( m/s (6.626x10-34 J.s)(3.00x10 8 = ( m/cm (1.20 cm)(10-2 = 1.66x10-23 J 12

13 ATOMIC SPECTRA What happen when an element is vaporized and then electrically excited? Light from excited Hydrogen atoms pases through a narrow slit and is then refracted by a prism. This light does not create a continuous spectrum, or rainbow, as sunlight does Instead, it creates a line spectrum, a series of fine lines of ( black ) individual colors separated by colorless spaces The wavelength of these spectral lines are characteristic of the element producing them Next the figure ==> 13

14 Example: The line spectra of hydrogen 14

15 Spectral Lines of Hydrogen Atom Spectroscopist studying the spectrum of atomic hydrogen had identified several series of such lines in different regions of the electromagnetic spectrum Three series of spectral lines of atomic hydrogen: 15

16 Rydberg Equation Rydberg Equation ==> to predict the position and wavelength of any lines in a given series: = R 2 2 λ n1 n2 where λ is the wavelength of a spectral line, n 1 and n 2 are positive integers with n 2 >n 1, and R is the Rydberg constant ( x10 7 m -1 ) For the visible series of lines, n 1 =2: 1 = R λ 1 2 1,withn =, n2 3,4,

17 The Bohr Model of The Hydrogen Atom Niels Bohr ( ) suggested a model for the H atom that predicted the existence of line spectra. In this model, Bohr used Planck's and Einstein's ideas about quantized energy and proposed three postulates: The H atom has only certain allowable energy levels ==> stationary states. Each of these states is associated with a fixed circular orbit of the electron around the nucleus The atom does not radiate energy while in one of its stationary states. That is, even though it violates the ideas of classical physics, the atom does not change energy while the electron moves within an orbit. The atom changes to another stationary state (the electron moves to another orbit) only by absorbing or emitting a photon whose energy equals the difference in energy between the two states: E photon = E state A E state B = hv 17

18 Quantum staircase of Hydrogen Atom 18

19 Bohr's Model A spectral line results when a photon of specific energy (and frequency) is emitted as the electron moves from a higher energy state to a lower one Therefore, Bohr's model explains that the atomic spectrum is not continuous because the atom's energy has only certain discrete levels or states In Bohr's model, the quantum number n is associated with the radius of an electron orbit, which is related to the electron's energy the lower the n value, the smaller the radius of the orbit, and the lower the energy level When the electron is in the first orbit (n=1), the orbit closest to the nucleus, the H atom is in its lowest energy level ==> GROUND STATE 19

20 Cont'd... If the H atom absorbs a photon whose energy equals the difference between the first and second energy levels, the electron moves to the second orbit (n=2), the next orbit out from the nucleus. When the electron is in the second or any higher orbit, the atom is said to be in an EXCITED STATE If the H atom in the first excited state (electron in second orbit) emits a photon of that same energy, it returns to the ground state. When electron drops from an outer orbit to an inner one, the atom emits a photon of specific energy that give rise to a spectral line ==> look at the next Figure 20

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22 Limitations of the Bohr's Model The Bohr Model failed to predict the spectrum of any other atom, even that of helium, the next simplest element. It suitable for H atom and for other one-electron species But, it does not work for atoms with more than one electron because in these systems, additional nucleus-electron attractions and electron-electron repulsions are present As a picture of the atom, the Bohr model is incorrect, but we still use the terms ground state and excited state. and retain one of Bohr's central ideas that: the energy of an atom occurs in discrete levels 22

23 The Energy States of the Hydrogen Atom Bohr's work ==> calculation of energy levels of an atom (which derived from principles of electrostatic attraction and circular 2 motion): 18 Z E = 2.18x10 J 2 n where Z is the charge of the nucleus Nuclear Charge 2 For H atom with Z=1: 1 18 E = 2.18x10 J = 2.18x10 J 2 n 18 1 Therefore, the energy of the ground state (n=1) is: E = 2.18x10 J = J x10 The negative sign appears because 1 we define the zero point of the atom's energy when the electron is completely removed from the nucleus Thus, E=0 when n=, so E<0 for any smaller n. 23 n 2

24 E = x10 J 2 n Z 2 24

25 The energy difference between any two levels: 1 ΔE = E final Einitial = 2.18x10 J 2 n final ninitial We can predict the wavelengths of the spectral lines of H atom: ΔE = hν = hc / λ = 2.18x10 J 2 2 Therefore (n final =n 2, n initial = n 1 ): n final n initial x10 J 1 1 = 2 2 λ hc n final n initial x10 J 1 1. = x10 J.s 3.00x10 m / s n final n initial = 1.10x10 m 2 2 n final n initial 25

26 Energy needed to completely remove the electron from an H atom: H(g) H + (g) + e - E=? n final = and n initial =1, and obtain: E is positive because energy is absorbed to remove the electron from the vicinity of the nucleus. For 1 mol of H atoms: x10 J ΔE = E final Einitial = ΔE = 2.18x10 J 01 = 2.18x10 kj / mol kJ 2.18x10 J / atom 6.022x10 atoms / mol ΔE = 3 10 J ΔE = 1.31x10 3 kj / mol This is the ionization energy of the H atom, the energy required to form 1 mol of gaseous H + ions from 1 mol of gaseous H atoms 26

27 de Broglie Wavelength From E=mc 2 and E=hv=hc/λ ==> de Broglie: wavelength of any particles: λ = h / mu Example: Find the de Broglie wavelength of an electron with a speed of 1.00x10 6 m/s (electron mass=9.11x10-31 kg; h=6.626x10-34 ( s / kg.m 2 λ = h mu = x10 34kg.m / s = 7.27x x10 31kg 1.00x10 m / s 10 m 27

28 The Heisenberg Uncertainty Principle Werner Heisenberg (1927) postulated the uncertainty principle. h Δx. m. Δu 4π Δx: the uncertainty in position; Δu: the uncertainty in speed. Example: An electron moving near an atomic nucleus has a speed of 6x10 6 m/s ± 1%. What is uncertainty in its position (Δx)? Solution: Finding uncertainty in speed, Δu: Δu = 1% of u = (0.01)(6x10 6 m/s) = 6x10 4 m/s Calculating the uncertainty in position, Δx: Δx h 4πmΔu 4π 6.626x10 34 kg.m / s x10 kg 6x10 m / s 3 Δx. m. Δu 1x10 9 h 4π m 28

29 Summary Blackbody radiation ==> Planck: Energy is quantized; only certain values allowed Photoelectric effect ==> Einstein: Light has particulate ( photons ) behavior Atomic line spectra ==> Bohr: Energy of atoms is quantized; photon emitted when electron changes orbit de Broglie: All matter travels in waves: energy of atom is quantized due to wave motion of electrons According to the uncertainty principle, we cannot know simultaneously the exact position and speed of an electron 29

30 QUANTUM-MECHANICAL MODEL OF THE ATOM GENERAL CHEMISTRY by Dr. Istadi 30

31 Quantum Mechanics? Dual nature of matter and energy The uncertainty principle The wave nature of objects on the atomic scale Quantum Mechanics Erwin Schrödinger (1926) ==> equation as the basis for the quantum-mechanical model of the hydrogen atom The model describes an atom that has certain allowed quantities of energy due to the allowed wavelike behavior of an electronwhose exact location is impossible to know 31

32 Atomic Orbital & Probable Location of Electron The electron's wave function (ψ, atomic orbital) is mathematical description of the electron's wavelike behavior in an atom Schrödinger Equation: H = E E: energy of atom; : wave function, H: Hamiltonian operator In complete form: 2 2 h d d + 2m 2 8pie dx dy d + dz V x, y,z ψx, y, z= Eψx, y,z Each wave function is associated with one of the atom's allowed energy states Each solution to the equation (each energy state of the atom) is associated with a given wave function ==> Atomic Orbital In Bohr's model, orbit was an electron's path around the nucleus 2 Here, orbital is mathematical function with no direct physical meaning 32

33 Electron Probability Density 33

34 An electron density diagram and a radial probability distribution plot show how the electron occupies the space near the nucleus for a particular energy level. We cannot know precisely where the electron is at any moment, but we can describe where it probably is, that is where it is most likely to be found Although the wave function (atomic orbital) has no direct physical meaning, the ψ 2 (probability density) measures the probability that the electron can be found within a particular tiny volume of the atom For a given energy level, we can depict this probability with an electron probability density diagram or an electron density diagram 34

35 Electron density diagram are called electron cloud The electron moves around the nucleus that would be appear as a cloud of electron positions. The electron cloud is an imaginary picture of the electron changing its position rapidly over time It does not mean that an electron is a diffuse cloud of charge The electron probability density decreases with distance from the nucleus along a line r. 35

36 Quantum Number of an Atomic Orbital When the atom absorbs energy, it exists in an excited state and the region of space occupied by the electron ==> a different atomic ( function orbital (wave An atomic orbital is specified by three quantum numbers: Principal Quantum Number (n): (..., 1,2,3 ) positive integer Indicates the relative size of the orbital and therefore the distance from the nucleus of the peak in the radial probability plot specifies the energy level of the H atom where the higher the n value, the higher the energy level. Example: H atom, when electron ==> n=1 ==> ground state ==> has lower energy; when electron ==> n=2 ==> excited state ==> has higher energy 36

37 Angular momentum quantum number (l): an integer from 0 to n-1 Indicates the shape of the orbital, sometimes called as orbital-shape quantum number n limits l Example: for orbital with n=1 ==> l=0; n=2 ==> l=0,1 Magnetic quantum number (m l ): an integer from -l through 0 to +l prescribes the orientation of the orbital in the space around the nucleus, sometimes called as orbital-orientation quantum number l sets the possible values of m l. Example: l=0 ==> m l =0; l=1 ==> m l =-1,0,+1 the number of possible m l values equals the number of orbitals, which is 2l+1 for a given l value. 37

38 Hierarchy of Quantum Numbers for Atomic Orbitals 38

39 The energy states and orbitals of the atom are described with specific terms and associated with one or more quantum numbers: 1. Level: the atom's energy levels, or shells, are given by the n value (the smaller the n value, the lower the energy level and the ( nucleus greater the probability of the electron being closer to the 2. Sublevel: the atom's levels contain sublevels, or subshells, which designate the orbital shape: l=0 is an s sublevel l=1 is a p sublevel l=2 is a d sublevel l=3 is a f sublevel s: sharp, p: principal, d: diffuse, f: fundamental The sublevel with n=2 and l=0 ==> 2s sublevel 39

40 3. Orbital: each allowed combination of n, l, and m l values specifies one of the atom's orbitals. Thus the three quantum numbers describes an orbital expressing its size (energy), shape, and spatial orientation. Example: from the hierarchy ==> n=2, l=0, and m l =0. Example: 3p sublevel has three orbitals: one with n=3, l=1, and m l =-1 another with n=3, l=1 and m l =0 and third with n=3, l=1, and m l =+1 Give the name, magnetic quantum number, and number of orbital for the following quantum numbers: n=3, l=2 n=2, l=0 n=5, l=1 40

41 Shapes of Atomic Orbitals: s Orbital The s orbital: l=0 spherical shape with nucleus at the center s orbital for H atom's ground state the electron probability density is ( 7.17A highest at the nucleus (Fig. Fig. 7.17B Because the 2s orbital is larger than the 1s, an electron in 2s spend more time farther from the nucleus than when it occupies the 1s. Fig. 7.17C the highest radial probability is at the greatest distance from the nucleus An s orbital has a spherical shape, so it can have only one orientation and, thus only one value for the magnetic quantum number: for any s orbital, m l =0 41

42 Figure

43 ( 2p The p Orbital (example: 43

44 An orbital with l=1 has two regions (lobes) of high probability, one on either side of the nucleus, and is called a p orbital. In the previous figure, the nucleus lies at the nodal plane of the dumpbell-shaped orbital. The maximum value of l is n-1 ==> only levels with n=2 of higher can have a p orbital. Therefore, the lowest energy p orbital is the 2p. Unlike an s orbital, each p orbital does have a specific orientation in space. The l=1 ==> m l = -1, 0, +1 ==> three mutually perpendicular p orbitals. They are identical in size, shape and energy, but differing only in orientation p orbital associates to x, y, and z axes ==> p x, p y, and p z 44

45 ( 3d The d Orbital (example: Radial probability distribution plot 45

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47 An orbital with l=2 is called a d orbital, with 5 possible m l values (-2, -1, 0, +1, +2). d orbital can have any one of five different orientations, as depicted in previous figure The following is one of the seven possible 4f orbitals: 47

48 Orbitals with Higher l Values Orbitals with l=3 are f orbitals and must have a principal quantum number at least n=4. There are seven f orbitals (2l + 1 = 7), each with a complex, multilobed shape Orbitals with l=4 are g orbitals, but they will not be discussed, because they play no known role in chemical bonding 48

49 Energy Levels of the Hydrogen Atom The energy state of the H atom depends on the principal quantum number n only. An electron in an orbital with a higher n value spends its time farther from the nucleus, so it is higher in energy Thus, in the case of H atom only, all four n=2 sublevels (one 2s and three 2p) have the same energy. and all nine n=3 sublevels (one 3s, three 3p, and five 3d) have the same energy LATIHAN SOAL-SOAL Pages: