Identify the quantum numbers of the electrons in atoms. Identify the periodical trend (radii, ionization energy, electronegativity)

Transcription

1 Chapter 7 Quantum Theory and Atomic Structure Key concepts Correlate the frequency, wavelength, and energy Apply Bohr model to identify the atomic spectrum Identify the quantum numbers of the electrons in atoms Derive the electron capabilities of energy level Determine the electron configuration Draw the orbital diagram for atoms or ions Identify the periodical trend (radii, ionization energy, electronegativity) Firework : Different color created by the atomic spectra of various elements Firework displays are fascinating to watch. Neon light transforms the skyline with brilliant color. Sodium vapor lamps transforms the skyline with brilliant color. 1. Light is electromagnetic radiation. Light travels through space as a wave which is made of successive crests and troughs. 2. The elementary particle that defines light is photon (wave and particle properties; it exhibits wave-particle duality). 3. The three basic dimensions of light are: Wave length (l) / Frequency (g) --perceived by humans as the color of the light. Intensity / amplitude (y) --related to the human perception of brightness the light. Polarization / angle of vibration described direction of their transverse electric field. 1

2 The Wave Nature Of Light Crest Trough amplitude Frequency and Wavelength Wavelength (λ) the distance between two consecutive crests most often measured in meter (m) or nanometer (nm) Frequency (γ) the number of wave cycles passing a given point in unit time. Unit Hz (a cycle per second) c = l n The speed of light can be determined by multiplying the length (l) of wave cycle by the number of cycles (g). Speed of light in vacuum : m/s Regions of the electromagnetic spectrum (EM) The EM of an object is the range of electromagnetic radiation that it emits, reflects, or transmits. The EM extends from the frequencies at the long-wavelength end (modern radio) to gamma radiation (at the short-wavelength end). The EM covers wavelengths from thousands of kilometers down to fractions of the size of an atom. The visible light to the eyes is only a small portion of the entire of EM spectrum. Ranging from 400 nm to 700 nm. (barbecue -charcoal -red light given off) 2

3 Interconverting Wavelength and Frequency PROBLEM: o A dental hygienist uses x-rays (λ = 1.00 A) to take a series of dental radiographs while the patient listens to a radio station (λ = 325 cm) and looks out the window at the blue sky( λ= 473 nm). What is the frequency (in s -1 ) of the electromagnetic radiation from each source? (Assume that the radiation travels at the speed of light, 3.00x10 8 m/s.) PLAN: Use equation c = λγ wavelength in units given o 1 A = m 1 cm = 10-2 m 1 nm = 10-9 m wavelength in m γ = c/λ frequency (s -1 or Hz) SOLUTION: 1.00A o m 1A o 325 cm 473nm 10-2 m 1 cm 10-9 m 1 nm g = g = g = = 1.00x10-10 m 3x10 8 m/s 1.00x10-10 m = 3x1018 s -1 = 325x10-2 m 3x10 8 m/s 325x10-2 m = 9.23x107 s -1 = 473x10-9 m 3x10 8 m/s = 6.34x10 14 s x10-9 m The particle nature of light wave-particle duality Black-body radiation and the quantization of energy The photoelectric effect and the photon theory Atomic spectra E = n h n The difference in atomic energy state: E = nhγ h is plank constant J s Blackbody radiation A hot and glowing object can emit or absorb a certain quantities of energy. The atoms have only certain quantities of energy (energy is quantized). When a solid object is heated to ca. 1000K, it begins to emit light. smoldering coal 1000 K soft red electric heating element 1500 K brighter, yellow light bulb filament 2000 K brighter and whiter 3

4 Take-home message The line spectra of several elements. Take-home message The Bohr explanation of the three series of spectral lines. 4

5 Take-home message Flame tests. strontium 38 Sr copper 29 Cu Emission and absorption spectra of sodium atoms. Quantum Numbers and Atomic Orbitals An atomic orbital is specified by three quantum numbers. n the principal quantum number -a positive integer l the angular momentum quantum number -an integer from 0 to n-1 m l the magnetic moment quantum number -an integer from -l to +l 5

6 The Hierarchy of Quantum Numbers for Atomic Orbitals Name, Symbol (Property) Allowed Values Quantum Numbers Principal, n (size, energy) Positive integer (1, 2, 3,...) Angular momentum, l (shape) 0 to n Magnetic, m l (orientation) -l,,0,,+l Summary of Quantum Numbers of Electrons in Atoms Name Symbol Permitted Values Property principal n positive integers(1,2,3, ) orbital energy (size) angular momentum l integers from 0 to n-1 orbital shape (The l values 0, 1, 2, and 3 correspond to s, p, d, and f orbitals, respectively.) magnetic m l integers from -l to 0 to +l orbital orientation spin m s +1/2 or -1/2 direction of e - spin 6

7 Sample Problem Determining Quantum Numbers for an Energy Level PROBLEM: What values of the angular momentum (l) and magnetic (m l ) quantum numbers are allowed for a principal quantum number (n) of 3? How many orbitals are allowed for n = 3? PLAN: Follow the rules for allowable quantum numbers found in the text. l values can be integers from 0 to n-1; m l can be integers from -l through 0 to + l. SOLUTION: For n = 3, l = 0, 1, 2 For l = 0 m l = 0 For l = 1 m l = -1, 0, or +1 For l = 2 m l = -2, -1, 0, +1, or +2 There are 9 m l values and therefore 9 orbitalswith n = 3. Orbital orentatin= n 2 Sample Problem Determining Sublevel Names and Orbital Quantum Numbers PROBLEM: Give the name, magnetic quantum numbers, and number of orbitalsfor each sublevel with the following quantum numbers: (a) n = 3, l = 2 (b) n = 2, l = 0 (c) n = 5, l = 1 (d) n = 4, l = 3 PLAN: Combine the n value and l designation to name the sublevel. Knowing l, we can find m l and the number of orbitals. SOLUTION: n l sublevel name possible m l values # of orbitals (a) 3 2 3d -2, -1, 0, 1, 2 5 (b) 2 0 2s 0 1 (c) 5 1 5p -1, 0, 1 3 (d) 4 3 4f -3, -2, -1, 0, 1, 2, 3 7 7

8 Atomic orbitals shape and size 1s 2s 3s s orbital s sublevels are spherical. The s orbital can take 2 electrons in total They differ from another in size. As n increases, the radius of orbital become larger. The 2p orbitals. The p orbitals P orbital consists two lobes along an axis (x,y,z). The p orbital can take 6 electrons in total. There is zero probability of finding electrons at the origin (the nucleus of the atom). Three orbitalsare oriented at the right angles to one another and designated as p x, p y, p z. 8

9 The 3d orbitals. The d orbitals There are five orbitalsin total. The d orbital can take 10 electrons in total. The d orbitalsare very influential when it comes to the transition metals. Take-home message 9

10 Take-home message One of the seven possible 4f orbitals. Take 14 electrons in total. Take-home message Different behaviors of waves and particles. 10

11 Take-home message The Schrödinger Equation HY = EY wave function mass of electron potential energy at x,y,z d 2 Y dx 2 d 2 Y d 2 Y + + 8p2 m + Q (E-V(x,y,z)Y(x,y,z) = 0 dy 2 dz 2 h 2 how ψ changes in space total quantized energy of the atomic system The photoelectric effect. Incoming EM radiation striking substance. Electrons flying off from a substance. The presence of a threshold frequency a beam of light consists of an enormous numbers of photons. light intensity is related to the # of photons striking the surface per unit time. the energy of the photon is absorbed by the electron and, if sufficient, the electron can escape from the material with a finite kinetic energy. a single photon can only eject a single electron, as the energy of one photon may only be absorbed by one electron. Absence of a time lag The electron can not save energy from several photons. One electron is ejected at the moment while it absorbs sufficient energy. 11

12 The hydrogen atom The H containing one electron. H play important role in developing modern electronic structure. The Bohr Model The Bohr assumed hydrogen consists of a central proton and an electron moves in a circular orbit. The Bohr model depicts the atom as a small, positively charged nucleus surrounded by waves of electrons orbit with electrostatic forces providing attraction, the waves spread over entire orbit The model's key success was in explaining the spectral emission lines of atomic hydrogen; The Bohr model is a primitive model of the hydrogen atom that cannot explain the fine structure of the hydrogen atom nor any of the heavier atoms. Three points of Bohr model Bohr designated 0 energy of an atom if the electron is completedremoved from the nucleus. Ordinary H has its lowest energy state, referred to as the ground state, n=1. When an excited electron gave off energy as a photon of light, it drops back to its ground state. 12