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The Electronic Structure of Atoms Electromagnetic Radiation Early atomic scientists studied the interaction of matter with electromagnetic radiation. Electromagnetic radiation, or radiant energy, includes visible light, infrared, micro and radio waves, and X-rays and ultraviolet light. Electromagnetic Radiation Electromagnetic radiation travels in waves. The waves of radiant energy have three important characteristics: 1. Wavelength - λ - (lambda) 2. Frequency – ν – (nu) 3. Speed – c – the speed of light Wavelength Wavelength, λ, is the distance between two adjacent peaks or troughs in a wave. The units may range from picometers to kilometers depending upon the energy of the wave. Frequency Frequency, ν, is the number of waves (or cycles) that pass a given point in space per second. The units are cycles/s, s-1 or hertz (Hz). The Speed of Light All electromagnetic radiation travels at the same speed. The speed of light ( c ) is: c = 2.9979 x 108 m/s Wavelength and Frequency Wavelength and frequency are inversely related. That is, waves with a low frequency have a long wavelength. Waves with a high frequency have short wavelengths. Properties of Light - Amplitude Diffraction Waves of electromagnetic radiation are bent or diffracted with they a passed through an obstacle or a slit with a size comparable to their wavelength. Electromagnetic Radiation The relationship between wavelength and frequency is: λν= c Matter and Energy By 1900, physicists thought that the nature of energy and matter was well understood and distinct. Matter, a collection of particles, have mass and a defined position in space. Radiant energy, as waves, is massless and delocalized. It was also believed that particles of matter could absorb or emit any energy, without restriction. Planck & Black Body Radiation Max Planck (1858-1947) studied the radiation emitted by objects heated until they glowed. He found that the energy emitted was not continuous, but instead was released in multiples of hν. ∆E = nhν where n=integer ν = frequency h = 6.626 x 10-34 J-s (Planck’s constant) Planck & Black Body Radiation ∆E = nhν Planck’s work showed that when matter and energy interact, the energy is quantized, and can occur only in discrete units or bundles with energy of hν. Each packet or bundle of energy is called a quantum. A fraction of a quantum is never emitted. Einstein – Photoelectric Effect Albert Einstein (1879-1955) won a Nobel Prize for his explanation of the photoelectric effect. When light of sufficient energy strikes the surface of a metal, electrons are emitted from the metal surface. Each metal has a characteristic minimum frequency, νo , called the threshold frequency, needed for electrons to be emitted. The Photoelectric Effect Observations 1. No electrons are emitted if the frequency of light used is less than νo, regardless of the intensity of the light. 2. For light with a frequency≥ νo , electrons are emitted. The number of electrons increases with the intensity of the light. 3. For light with a frequency > νo , the electrons are emitted with greater kinetic energy. Explanation Einstein proposed that light is quantized, consisting of a stream of “particles” called photons. If the photon has sufficient energy, it can “knock off” an electron from the metal surface. If the energy of the photon is greater than that needed to eject an electron, the excess energy is transferred to the electron as kinetic energy. The Photoelectric Effect Ephoton= hν = hc/λ If incident radiation with a frequency νi is used: KEelectron = hνi -hνo = ½ mv2 The kinetic energy of the electron equals the energy of the incident radiation less the minimum energy needed to eject an electron. Particle-Wave Duality Einstein’s work suggested that the incident photon behaved like a particle. If it “hits” the metal surface with sufficient energy (hνi), the excess energy of the photon is transferred to the ejected electron. In the atomic scale, waves of radiant energy have particle-like properties. Particle-Wave Duality Einstein also combined his equations: E=mc2 with Ephoton= hc/λ to obtain: hc/λ E m= 2 = c2 c h m= λc Particle-Wave Duality The apparent mass of radiant energy can be calculated. Although a wave lacks any mass at rest, at times, it behaves as if it has mass. Einstein’s equation was confirmed by experiments done by Arthur Compton in 1922. Collisions between X-rays and electrons confirmed the “mass” of the radiation. Louis de Broglie Einstein showed that waves can behave like particles. In 1923, Louis de Broglie (1892-1987) proposed that moving electrons have wave-like properties. Louis de Broglie Using Einstein’s equation: m=h/λv where v is the velocity of the particle, de Broglie rearranged the equation to calculate the wavelength associated with any moving object. Louis de Broglie λ=h/mv de Broglie’s equation was tested using a stream of electrons directed at a crystal. A diffraction pattern, due to the interaction of waves, resulted. The experiment showed that electrons have wave-like properties. Wave-Like Nature of the Electron Particle-Wave Duality It is important to note that the wavelike properties of moving particles are insignificant in our everyday world. A moving object such as a car or a tennis ball has an incredibly small wavelength associated with it. It is on the atomic scale that the dual nature of particles and light become significant. Emission Spectrum of Hydrogen When atoms are given extra energy, or excited, they give off the excess energy as light as they return to their original energy, or ground state. H2 Hg He Emission Spectrum of Hydrogen Scientists expected atoms to be able to absorb and emit a continuous range of energies, so that a continuous spectrum of wavelengths would be emitted. Emission Spectrum of Hydrogen A continuous spectrum in the visible range, would look like a rainbow, with all colors visible. Instead, hydrogen, and other excited atoms emit only specific wavelengths of light as they return to the ground state. A line spectrum results. Emission Spectrum of Hydrogen Emission Spectrum of Hydrogen Instead, only a few wavelengths of light are emitted, creating a line spectrum. The spectrum of hydrogen contains four very sharp lines in the visible range. Emission Spectrum of Hydrogen The discrete lines in the spectrum indicate that the energy of the atom is quantized. Only specific energies exist in the excited atom, so only specific wavelengths of radiation are emitted. The Bohr Atomic Model In 1913, Niels Bohr (1885-1962) proposed that the electron of hydrogen circles the nucleus in allowed orbits. That is, the electron is in its ground state in an orbit closest to the nucleus. As the atom becomes excited, the electron is promoted to an orbit further away from the nucleus. The Bohr Atomic Model Classical physics dictates that an electron in a circular orbit must constantly lose energy and emit radiation. Bohr proposed a quantum model, as the spectrum showed that only certain energies are absorbed or emitted. The Bohr Atomic Model Bohr’s model of the hydrogen atom was consistent with the emission spectrum, and explained the distinct lines observed. The Bohr Atomic Model The Bohr Atomic Model Bohr also developed an equation, using the spectrum of hydrogen, that calculates the energy levels an electron may have in the hydrogen atom: E=-2.178 x 10-18J(Z2/n2) Where Z = atomic number n = an integer The Bohr Atomic Model The Bohr model didn’t work for atoms other than hydrogen. Though limited, Bohr’s approach did attempt to explain the quantized energy levels of electrons. Later developments showed that any attempt to define the path of the electron is incorrect. The Quantum Mechanical Model The quantum mechanical atomic model was developed based on the theories of Werner Heisenberg (1901-1976), Louis de Broglie (18921987) and Erwin Schrödinger (1887-1961). They focused on the wave-like nature of the moving electron. The Quantum Mechanical Model The electron in an atom was viewed as a standing wave. For an energy level to exist, the wave must reinforce itself via constructive interference. The Quantum Mechanical Model Schrödinger developed complex equations called wave functions ( Ψ). The wave functions can be used to calculate the energy of electrons, not only in hydrogen, but in other atoms. The Quantum Mechanical Model The wave functions also describe various volumes or spaces where electrons of a specific energy are likely to be found. These spaces are called orbitals. The Quantum Mechanical Model Orbitals are not orbits. The wave functions provide no information about the path of the electron. Instead, it provides the space in which there is a high probability (90%) of finding an electron with a specific energy. The Heisenberg Uncertainty Principle Werner Heisenberg showed that, due to the wave nature of the electron, It is impossible to know both the precise position and the momentum of the electron at the same time. This is known as the Heisenberg Uncertainty Principle. The Heisenberg Uncertainty Principle It is impossible to know both the precise position and the momentum of the electron at the same time. In mathematical terms, the principle is: (Δx) (Δmv) ≥ (h/4π) The Heisenberg Uncertainty Principle It is impossible to know both the precise position and the momentum of the electron at the same time. The Heisenberg Uncertainty Principle (Δx) (Δmv) ≥ (h/4π) There is a limit to how well we can determine position (x), if mass and velocity are known precisely. For large particles, the uncertainty is insignificant. However, on the atomic scale, we cannot know the exact motion of an electron. The Heisenberg Uncertainty Principle (Δx) (Δmv) ≥ (h/4π) For an electron in a hydrogen atom, the uncertainty in the position of the electron is similar in size to the entire hydrogen atom. Thus the location of the electron cannot be determined. Orbitals The Schrödinger equation is used to describe the space in which it is likely to find an electron with a specific energy. The equation provides us with a probability distribution, or an electron density map. It is important to remember that the resulting shape does not give us any information about the path of the electrons. Orbitals The orbital of lowest energy is the 1s orbital. The probability distribution shows electron density in all directions, creating a spherical shape. Orbitals Orbitals The first energy level of hydrogen (n=1) consists of a 1s orbital. The second energy level of hydrogen (n=2) consists of a 2s orbital and 2p orbitals. The third energy level of hydrogen (n=3) consists of a 3s orbital, 3p orbitals, and 3d orbitals. Orbitals As the value of n increases, the orbitals, on average, become larger, with more electron density farther from the nucleus. Orbitals The “white rings” in the drawings are nodes. This is the region where the wave function goes from a positive value to a negative value. Orbitals p orbitals are “dumbbell” shaped, with two lobes. In one lobe, the wave function is positive, in the other lobe, it is negative. Orbitals p orbitals come in sets of three, called a subshell. The three orbitals are designated as px, py and pz, because the electron density lies primarily along either the x, y or z axis. Orbitals All three orbitals have the exact same energy. Orbitals with the same energy are called degenerate. Orbitals The n=3 level contains s, p and d orbitals. The d orbitals are shown. Orbitals The n=4 level contains s, p, d and f orbitals. The f orbitals are shown. Quantum Numbers In addition to n, the principal quantum number, there are three additional quantum numbers which describe the type of orbital ( l ) , the spatial orientation of the orbital (ml ) , and the spin of the electron (ms ) . Energy Levels In any atom or ion with only 1 electron, the principal quantum number, n, determines the energy of the electron. For n=2, the 2s and 2p orbitals all have the same energy. Energy Levels Likewise, the 3s, 3p and 3d orbitals are all degenerate, with the same energy. Energy Levels In a multi-electron atom, there is interaction between electrons. As a result of this interaction, the various subshells of a principal quantum level will vary in energy. Energy Levels Energy Levels Energy Levels The energy diagram for the first three quantum levels shows the splitting of energies. Energy Levels For a given value of n, the energies of the subshells is as follows: ns<np<nd<nf Energy Levels The subshells have different energies due to the penetrating ability for each type of orbital. Electrons in a 2s orbital can get nearer to the nucleus than those in a 2p orbital. Energy Levels The electrons in the 3s orbital (top diagram) have higher probability to be found near the nucleus, and thus greater penetrating ability than those in 3p or 3d orbitals. Multi-electron Atoms Orbitals of any type can be empty, or have 1 or two electrons. Experimental data indicate that if two electrons are in the same orbital, they will spin in opposite directions. Multi-electron Atoms Electron configurations are a way of noting which subshells of an atom contain electrons. Although much of the periodic table was developed before the concept of electron configurations, it turns out that the position of an element on the periodic table is directly related to its electron configuration. Multi-electron Atoms Magnetic Properties of Atoms Rotating electrons create a magnetic field. If electrons are unpaired, the atom will be attracted to a magnetic field and be paramagnetic. If all of the electrons in an atom are paired, the atom will be weakly repelled by a magnetic field, and be diamagnetic. Magnetic Properties of Atoms Hund’s Rule states that electrons will occupy degenerate orbitals singly with parallel spins. The Pauli Exclusion Principle states that two electrons occupying the same orbital will have opposite spins. Representation of Orbitals Orbitals are usually represented by a horizontal line, with the electrons appearing as arrows. Arrows up and down indicate electrons of opposite spins. Multi-electron Atoms The electron configuration for N is: 1s22s22p3 N atoms have 3 unpaired electrons: __ __ __ Multi-electron Atoms The electron configurations for Cr and Cu differ from that expected based on their positions in the periodic table. Cr and Cu The electron configuration for Cr is: [Ar] 4s13d5 with 6 unpaired electrons The electron configuration for Cu is: [Ar] 4s13d10 with the unpaired electron in the 4s orbital Valence Electrons The electrons in the highest occupied quantum level are called valence electrons. These are the electrons that are involved in bonding. Elements in the same family or group all have the same number of valence electrons and thus exhibit similar chemical behavior. Valence Electrons All of the group IA elements have a single valence electron (ns1). Group IIA elements have two valence electrons, etc. The noble gases all have eight valence electrons(ns2np6). When the main group elements form ions, they usually lose or gain enough electrons to attain the same electron configuration as a noble gas. Periodic Trends Many of the properties of atoms show clear trends in going across a period (from left to right) or down a group. In going across a period, each atom gains a proton in the nucleus as well as a valence electron. Periodic Trends The increase of positive charge in the nucleus isn’t completely cancelled out by the addition of the electron. Electrons added to the valence shell don’t shield each other very much. As a result, in going across a period, the effective nuclear charge (Zeff) increases. Effective Nuclear Charge The effective nuclear charge (Zeff) equals the atomic number (Z) minus the shielding factor (σ). Zeff= Z-σ Effective Nuclear Charge Zeff= Z-σ Effective Nuclear Charge Electrons in the valence shell are partially shielded from the nucleus by core electrons. Effective Nuclear Charge Electrons in p or d orbitals don’t get too close to the nucleus, so they are less shielding than electrons in s orbitals. As a result, effective nuclear charge increases across a period. Periodic Trends In going down a group or family, a full quantum level of electrons, along with an equal number of protons, is added. As n increases, the valence electrons are, on average, farther from the nucleus, and experience less nuclear pull due to the shielding by the “core” electrons. As a result, Zeff decreases slightly going down a group. Periodic Trends Trends- Atomic Radii Atomic radii are obtained in a variety of ways: 1. For metallic elements, the radius is half the internuclear distance in the crystal, which is obtained from X-ray data. 2. For diatomic molecules, the radius is half the bond length. 3. For other elements, estimates of the radii are made. Trends- Atomic Radii Atomic radii follow trends directly related to the effective nuclear charge. As Zeff increases across a period, the electrons are pulled closer to the nucleus, and atomic radii decrease. As Zeff decreases down a group, the valence electrons experience less nuclear attraction, and the radius increases. TrendsAtomic Radii Atomic size roughly halves across a period, and doubles going down a group.