Chapter 5 Periodicity and the Electronic Structure of Atoms

A Theory that Explains Electron Behavior the quantum-mechanical model explains the manner electrons exist and behave in atoms helps us understand and predict the properties of atoms that are directly related to the behavior of the electrons why some elements are metals while others are nonmetals why some elements gain 1 electron when forming an anion, while others gain 2 why some elements are very reactive while others are practically inert and other Periodic patterns we see in the properties of the elements

The Nature of Light its Wave Nature One of the ways that energy travels through space: – Light from sun; microwave oven; radiowaves for MRI mapping • Exhibit the same type of wavelike behavior and travel at the speed of light in a vacuum • It has electric and magnetic fields that simultaneously oscillate in planes mutually perpendicular to each other and to the direction of propagation through space. Electromagnetic radiation has oscillating electric (E) and magnetic (H) fields in planes

The Nature of Light its Wave Nature light is 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 an magnetized particle experiences a force all electromagnetic waves move through space at the same, constant speed 3.00 x 108 m/s in a vacuum = the speed of light, c

Characterizing Waves the number of waves = number of cycles Waves are characterized by wavelength, frequency, and speed. – wavelength (λ) is the distance between two consecutive peaks or troughs in a wave. – frequency (ν) is defined as the number of waves (cycles) per second - is a measure of the distance covered by the wave the distance from one crest to the next the number of waves = number of cycles units are hertz, (Hz) or cycles/s = s-1 1 Hz = 1 s-1 the amplitude is the height of the waVe the distance from node to crest or node to trough the amplitude is a measure of how intense the light is – the larger the amplitude, the brighter the light

Amplitude & Wavelength Dim light Bright light

The Electromagnetic Spectrum visible light comprises only a small fraction of all the wavelengths of light – called the electromagnetic spectrum short wavelength (high frequency) light has high energy radiowave light has the lowest energy gamma ray light has the highest energy high energy electromagnetic radiation can potentially damage biological molecules ionizing radiation l 

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 since the speed of light is constant, if we know wavelength we can find the frequency, and visa versa c = v x λ c is defined to be the rate of travel of all electromagnetic energy in a vacuum and is a constant value—speed of light. c= 3.00 x 108 m/s

Example Calculate the wavelength of red light with a frequency of 4.62 x 1014 s-1 A laser dazzels the audience in a rock concert by emitting green light with a wave length of 515 nm. Calculate the frequency of the light

Particlelike Properties of Radiant Energy: The Photoelectric Effect and Planck’s Postulate 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 waves intensity made brighter, more electrons should be ejected the frequency of the light used for the irradiation must be above some threshold value, which is different for every metal called the threshold frequency regardless of the intensity it was also observed that high frequency light with a dim source caused electron emission without any lag time

Particlelike Properties of Radiant Energy: The Photoelectric Effect and Planck’s Postulate Refers to the phenomenon in which electrons are emitted from the surface of a metal when light strikes it: – No electrons are emitted by a given metal below a specific threshold frequency νo. – For light with frequency lower than the threshold frequency, no electrons are emitted regardless of the intensity of the light. – For light with frequency greater than the threshold frequency, the number of electrons emitted increases with the intensity of the light. – For light with frequency greater than the threshold frequency, the kinetic energy of the emitted electrons increases linearly with the frequency of the light.

Einstein’s Explanation Energy is in fact quantized and can be transferred only in discrete units of size hν. A system can transfer energy only in whole quanta Einstein proposed that the light energy was delivered to the atoms in packets, called quanta or photons the energy of a photon of light was directly proportional to its frequency inversely proportional to it wavelength the proportionality constant is called Planck’s Constant, (h) and has the value 6.626 x 10-34 J∙s

Examples What is the energy (in kJ/mol) of photons of radar waves with ν = 3.35 x 108 Hz? Calculate the number of photons in a laser pulse with wavelength 337 nm and total energy 3.83 mJ

The Bohr Model of the Atom: Quantized Energy Neils Bohr proposed that the electrons could only have very specific amounts of energy fixed amounts = quantized the electrons traveled in orbits that were a fixed distance from the nucleus stationary states therefore the energy of the electron was proportional the distance the orbital was from the nucleus electrons emitted radiation when they “jumped” from an orbit with higher energy down to an orbit with lower energy the distance between the orbits determined the energy of the photon of light produced

The Interaction of Radiant Energy with Atoms: Line Spectra In 1885, Johann Balmer discovered a mathematical relationship for the four visible lines in the atomic line spectrum for hydrogen. l 1 = R n2 22 − Line Spectrum: A series of discrete lines on an otherwise dark background as a result of light emitted by an excited atom

The Bohr Model of the Atom: Quantized Energy Johannes Rydberg later modified the equation to fit every line in the entire spectrum of hydrogen. m: shell the transition is to (inner shell) l 1 = R n2 m2 − n: shell the transition is from (outer shell)

Wavelike Properties of Matter Chapter 5: Periodicity and Atomic Structure Wavelike Properties of Matter 1/13/2019 Energy is really a form of matter, and all matter exhibits both particulate and wave properties. –Large “pieces” of matter, such as base balls, exhibit predominantly particulate properties –Very small “pieces” of matter, such as photon, while showing some particulate properties through relativistic effects, exhibit dominantly wave properties –“Pieces” of intermediate mass, such as electrons, show both the particulate and wave properties of matter Louis de Broglie in 1924 suggested that, if light can behave in some respects like matter, then perhaps matter can behave in some respects like light. In other words, perhaps matter is wavelike as well as particlelike. mv h l = Copyright © 2008 Pearson Prentice Hall, Inc.

examples What velocity would an electron (mass = 9.11 x 10-31kg) need for its de Broglie wavelength to be that of red light (750 nm)? Determine the wavelength of a neutron traveling at 1.00 x 102 m/s (Massneutron = 1.675 x 10-24 g)

Quantum Mechanics and the Heisenberg Uncertainty Principle Heisenberg Uncertainty Principle – both the position (Δx) and the momentum (Δmv) of an electron cannot be known beyond a certain level of precision 1. (Δx) (Δmv) > h 4π 2. Cannot know both the position and the momentum of an electron with a high degree of certainty 3. If the momentum is known with a high degree of certainty i. Δmv is small ii. Δ x (position of the electron) is large 4. If the exact position of the electron is known i. Δmv is large ii. Δ x (position of the electron) is small

The Quantum Mechanical Model of the Atom: Orbitals and Quantum Numbers electron energy and position are complimentary because KE = ½mv2 for an electron with a given energy, the best we can do is describe a region in the atom of high probability of finding it – called an orbital a probability distribution map of a region where the electron is likely to be found distance vs. y2 (wave function) many of the properties of atoms are related to the energies of the electrons Probability of finding electron in a region of space (Y 2) Solve Wave equation Wave function or orbital (Y) calculations show that the size, shape and orientation in space of an orbital are determined 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 Since we can’t ever be certain of the electron’s position, we work with probabilities.

The Quantum Mechanical Model of the Atom: Orbitals and Quantum Numbers Principal Quantum Number (n) Describes the size and energy level of the orbital Commonly called a shell Positive integer (n = 1, 2, 3, 4, …) As the value of n increases, the energy increases. the average distance of the e– from the nucleus increases.

The Quantum Mechanical Model of the Atom: Orbitals and Quantum Numbers Angular-Momentum Quantum Number (l) Defines the three-dimensional shape of the orbital Commonly called a subshell There are n different shapes for orbitals. If n = 1, then l = 0. If n = 2, then l = 0 or 1. If n = 3, then l = 0, 1, or 2. Commonly referred to by letter (subshell notation) l = 0 s (sharp) l = 1 p (principal) l = 2 d (diffuse) l = 3 f (fundamental) Scientists working in spectroscopy first used sharp, principal, diffuse, and fundamental with respect to atomic spectra. After f, the series goes alphabetically (g, h, etc.). the energy of the subshell increases with l (s < p < d < f).

The Quantum Mechanical Model of the Atom: Orbitals and Quantum Numbers Magnetic Quantum Number (ml ) Defines the spatial orientation of the orbital There are 2l + 1 values of ml, and they can have any integral value from -l to +l. If l = 0, then ml = 0. If l = 1, then ml = –1, 0, or 1. If l = 2, then ml = –2, –1, 0, 1, or 2.

The Quantum Mechanical Model of the Atom: Orbitals and Quantum Numbers

Examples Give the possible combination of quantum numbers for the following orbitals 3s orbital 2 p orbitals Give orbital notations for electrons in orbitals with the following quantum numbers: n = 2, l = 1 ml = 1 n = 3, l = 2, ml = -1

The Shapes of Orbitals Node: A surface of zero probability for finding the electron s orbitals are spherical and penetrate closer to the nucleus.

The Shapes of Orbitals p orbitals are dumbbell-shaped, with a nodal plane running through the nucleus. Introductory Physical Chemistry courses often explore the mathematical relationships that define the regions of space (or shape).