Chapter 7 Atomic Structure and the periodic table

Characterestics Of Light Spectroscopy is the study of the interaction between radiation (electromagnetic radiation, or light, as well as particle radiation) and matter. Spectrometry is the measurement of these interactions and an instrument which performs such measurements is a spectrometer or spectrograph. A plot of the interaction is referred to as a spectrum.

The spectrum of colors emitted by atoms that have been heated to high temperatures is called an atomic emission spectrum. Light is electromagnetic radiation, a wave of electric and magnetic field that travels at the speed of light(3. 00 х108 m/s).

Dispersion of light as it passes through a prism

Light waves travel at a constant speed. Because of this there is a one to one relationship between light's wavelength and its frequency. If waves are short, there must be more of them in a set amount of time to travel the same distance in that time (the same speed). The unit of frequency is Hertz(Hz) 1 Hz=1 cycle/sec

The intensity of the light is proportional to the square of the amplitude of the wave. The distance between adjacent peaks gives its wavelength, λ. λ=c/ν

Our eyes detect electromagnetic radiation with wavelengths from 700 nm(red light) to 400 nm(violet light). The electromagnetic radiation in this range is called as visible light. Ultraviolet radiation(UV) has a frequency higher than that of violet light; its wavelength is less than about 400 nm. Infrared radiation(IR) has a frequency lower than that of red light ; its wavelength is greater than about 800 nm. Microwaves, used in radars and microwave ovens, have wavelengths in the millimeter to centimeter range.

Class Practice What is the wave length of orange light of frequency 4. 8 х1014 Hz?

Quanta and photon Electromagnetic radiation is a stream of many packets of electromagnetic energy. These packets are called as photons. The photon is the elementary particle responsible for electromagnetic phenomena. The photon travels (in vacuum) at the speed of light, c. Energy is transferred in discrete amounts called as quantum(plural quanta) Like all quanta, the photon has both wave and particle properties (“wave particle duality “). The more intense the light the greater the number of photons passing a given point each second. The relation between the energy , E of a photon and the frequency ν, of the radiation as E=hν where h is Plank’s constant, with a value of 6. 63 х10 -34 J. s

Class Practice What is the energy in kilojoules per mole of photons of amber light of frequency 5. 2 х1014 Hz? A student’s favorite radio station broadcasts a signal at a frequency of 91. 5 MHz. What is the energy of the photon’s broadcast?

Home work Page 314 7. 12, 7. 14 and 7. 18

Atomic Spectra and energy levels The Lyman series is the wavelengths in the ultraviolet (UV) spectrum of the hydrogen atom, resulting from electrons dropping from higher energy levels into the n = 1 orbit. The Balmer series is the wavelengths in the visible light spectrum of the hydrogen atom, resulting from electrons falling from higher energy levels into the n = 2 orbit. The Paschen series is the wavelengths in the infrared spectrum of the hydrogen atom, resulting from electrons falling from higher energy levels into the n = 3 orbit.

Rydberg formula for hydrogen Where λvac is the wavelength of the light emitted in vacuum, RH is the Rydberg constant for hydrogen.

Bohr’s atom The Bohr model of the hydrogen atom where negatively charged electrons confined to atomic shells encircle a small positively charged atomic nucleus, and that an electron jump between orbits must be accompanied by an emitted or absorbed amount of electromagnetic energy hν. The orbits that the electrons travel in are shown as grey circles; their radius increases n 2, where n is the principal quantum number. The 3→ 2 transition depicted here produces the first line of the Balmer series, and for hydrogen (Z = 1) results in a photon of wavelength 656 nm (red).

Wavelike properties of electrons Louis-Victor formulated the de Broglie hypothesis, claiming that all matter, not just light, has a wave-like nature; he related wavelength (denoted as λ ), and momentum (denoted as p): This is a generalization of Einstein's equation above, since the momentum of a photon is given by p=E/c and the wavelength by λ=c/f, where c is the speed of light in vacuum.

Class Practice Calculate the wavelength of a marble of mass 5. 00 g traveling at 1. 00 m/s.

Models Of Atoms Our current model of a hydrogen atom was proposed by the Austrian scientist Erwin Schrodinger. He devised an equation (Schrodinger’s Equation)that enabled him to calculate the shape of the wave associated with any particle. Quantum theory is based on Schrodinger's equation; Hψ=Eψ in which electrons are considered as wave-like particles whose "waviness" is mathematically represented by a set of wave functions ψ, obtained by solving Schrodinger's equation.

Atomic orbitals The wave function for an electron is so important that it is given a special name an atomic orbital. Atomic orbitals have characterestic energy and shapes. The different shapes are identified by different letters. An s orbital is a spherical cloud that becomes less dense as the distance from the nucleus increases. p-orbital is a cloud with two lobes on opposite sides of the nucleus. The lobes are separated by a nodal plane. The d and f orbital have complicated shapes.

The shapes of different orbitals As for p-orbital the opposite shades of color denote opposite signs of wave. The location of an electron is best described as a cloud of probable locations.

Home work Page 314 7. 30, 7. 34, 7. 36

Energy levels Each orbital has a characteristic energy. When Schrodinger solved his equation, he found that the allowed energies of the electron in a hydrogen atom are given by the expression E=-h. RH /n² n=1, 2… RH, is called as the Rydberg’s constant. The experimental value of Rydberg’s constant=3. 29 х1015 Hz Whenever the atom emits a photon of radiation, the energy emitted is equal to the difference in two of the allowed energy levels. Each transition corresponds to a line in the spectrum of atomic hydrogen.

Class Practice Calculate the wavelength of a photon emitted by a hydrogen atom when an electron makes a transition from an orbital with n=3 to one with n=2.

Quantum Numbers Schrodinger found that each atomic orbital is identified by three numbers called quantum numbers. The quantum number n is called the principal quantum number. The orbital angular momentum quantum number, l, specifies the shape of the orbital. The magnetic quantum number, ml specifies the individual orbital of a particular shape.

An orbital is specified by three quantum numbers; orbitals are organized into shells and subshells. An electron has the property of spin ; the spin is described by the quantum number ms which may have one of the two values.

Class Practice Calculate with n=6. the total number of orbitals in a shell

Orbital energies In a many-electron atom, because of the effects of penetration and shielding, s-electrons have a lower energy than p-electrons of the same shell; the order of increasing orbital energies within a given shell is s<p<d<f.

Pauli’s Exclusion Principle No more than two electrons may occupy any given orbital. When two electrons do occupy one orbital, their spins must be paired.

Hund’s Rule If more than one orbital in a subshell is available, electrons will fill empty orbitals before pairing in one of them.

The ground state electron configuration of an atom of an element with atomic number Z is predicted by adding Z electrons to available orbitals so as to obtain the lowest total energy.

Class Practice Predict the ground state electron configuration of a sulfur atom and draw the box diagram. Predict the ground state electron configuration of a magnesium atom.

Electron configuration of an ion. To predict the electron configuration of a cation , remove outermost electrons in the order np, ns, and(n-1)d For an anion, add electrons until the next noble gas configuration has been reached.

Home work Page 315 7. 42, 7. 44, 7. 48,

Periodicity of Atomic Properties Atomic radius: The atomic radius is defined as half the distance between the centers of neighboring atoms. Atomic radii generally increase down a group and decrease from left to right.

Ionic radius The ionic radius of an element is its share of the distance between neighboring ions in an ionic solid. Ionic radii generally increase down a group and decrease from left to right across a period. Cations are smaller than their parent atoms and anions are larger.

Class Practice Arrange each pair of ions in order of increasing ionic radius: (a)Mg 2+ and Ca 2+ (b)O 2 - and F-

Ionization energies The ionization energy of an element is the energy needed to remove an electron from an atom of the element in the gas phase. For the first ionization energy we start with a neutral atom.

First and second ionization energies For the first ionization energy, I 1, we start with the neutral atom, for example, for copper, Cu(g) Cu+(g) +e-(g) I 1 =(energy of Cu+ +e-)-(energy of Cu) The experimental value for copper is 785 k. J/mol. The second ionization energy I 2 is the energy required to remove an electron from a singly charged gas phase cation. For copper Cu+(g) Cu 2+(g) + e-(g) I 2=(energy of Cu 2+ +e-)-(energy of Cu+)For copper I 2 =1958 k. J/mol

The second ionization energy is always greater than the first because once the first electron is pulled off, you are now trying to remove the second electron from a positively charge ion. Because of the electrostatic attraction between + and -, it is more difficult to pull an electron away from a positively charge ion than a neutral atom.

The first ionization energy is highest for elements close to helium and is lowest for elements close to cesium. Second ionization energies are higher than first ionization energies (of the same element). An ionization energy is very high if the electron is to be expelled from a closed shell.

Electron affinity The electron affinity is a measure of the energy change when an electron is added to a neutral atom to form a negative ion. For example, when a neutral chlorine atom in the gaseous form picks up an electron to form a Cl- ion, it releases an energy of 349 k. J/mol or 3. 6 e. V/atom. An electron affinity of -349 k. J/mol and this large number indicates that it forms a stable negative ion. Small numbers indicate that a less stable negative ion is formed. Groups VIA and VIIA in the periodic table have the largest electron affinities.

Elements with the highest electron affinities are those close to oxygen, fluorine, and chlorine. Group 17 atoms can acquire one electron with a release of energy and group 16 atoms can accept two electrons with chemically attainable energies. The halogens typically form X- ions and group 16 elements form X 2 - ions.

Diagonal relationship On moving diagonally across the periodic table, the elements show certain similarities in their properties which are quite prominent in some cases as shown below. This is called a diagonal relationship.

. A Diagonal Relationship is said to exist between certain pairs of diagonally adjacent elements in the second and third periods of the periodic table. These pairs (Li & Mg, Be & Al, B & Si etc. ) exhibit similar properties; for example, Boron and Silicon are both semiconductors form halides that are hydrolysed in water and have acidic oxides. Such a relationship occurs because crossing and descending the periodic table have opposing effects. On crossing a period of the periodic table, the size of the atoms decreases, and on descending a group the size of the atoms increases. Similarly, on moving along the period the elements become progressively more covalent, less reducing and more electronegative whereas on descending the group the elements become more ionic, more basic and less electronegative.

Thus, on both descending a group and crossing by one element the changes cancel each other out, and elements with similar properties which have similar chemistry are often found - the atomic size, electronegativity, properties of compounds (and so forth) of the diagonal members are similar.

Homework Page 315 7. 62, 7. 64, Page 316 7. 70, 7. 78, 7. 80, 7. 90