Chapter 1 Atomic Structure

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CHAPTER 1: ATOMIC STRUCTURECHEM210/Chapter 1/2014/01An atom is the smallest unit quantity of an element that can exist on its own or can combine chemically with other atoms of the same or another element.Composed of protons, neutrons and electrons.

CHEM210/Chapter 1/2014/02NUCLIDES, ATOMIC NUMBER AND MASS NUMBERA nuclide is a particular type of atom and has a characteristic atomic number, Z.The mass number, A, of a nuclide is the number of protons and neutrons in the nucleus.element symbolatomic numbermass numberRELATIVE ATOMIC MASSISOTOPESSame number of protons and electrons but different mass numbers.ATOMIC NUMBER, MASS NUMBER AND ISOTOPES

CHEM210/Chapter 1/2014/03EXAMPLESOLUTIONThe relative atomic masses of chlorine is the weighted mean of the mass numbers of the two isotopes.EXERCISE FOR THE IDLE MINDIf Ar for Cl is 35.45, what is the ratio of the two isotopes present in a sample of Cl atoms containing naturally occurring Cl?

CHEM210/Chapter 1/2014/04QUANTUM THEORYDevelopment of quantum theory took place in two steps; in the older theories, the electron was treated as a particle. In more recent models, the electron is treated as a wave, hence wave mechanics.A quantum of energy is the smallest quantity of energy that can be emitted (or absorbed) in the form of electromagnetic radiation (Planck-1901).The energy, E, is given by:where h = Plancks constant = 6.626 10-34 JsOne of the important applications of early quantum theory was the Rutherford- Bohr model of the hydrogen atom.

CHEM210/Chapter 1/2014/05Balmer (1885) wavelength of the spectral lines of hydrogen obeyed the equation: The various series in atomic H emission spectrumSeries n n RegionLyman12,3,4, .UV Balmer23,4,5, . Visible Paschen34,5,6, .IR Brackett45,6,7, .IR Pfund56,7,8, .IR

BOHRS THEORY OF THE ATOMIC SPECTRUM OF HYDROGENCHEM210/Chapter 1/2014/06Bohr (1913) stated two postulates for an electron in an atom:Stationary states exist in which the energy of the electron is constant and such states are characterized by circular orbits about the nucleus in which the electron has an angular momentum, mvr give by the equation:where m = mass of electron, v = velocity of electron, r = radius of the orbit and h = Planck constantEnergy is absorbed or emitted only when an electron moves from one stationary state to another and the energy change is given by:where n1 and n2 are the principal quantum numbers.

CHEM210/Chapter 1/2014/07If we apply the Bohr model to the hydrogen atom, the radius of each allowed circular orbit can be determined from the equation:where o = permittivity of a vacuum = 8.854 10-12 F m-1For n = 1, the radius for the first orbit of the H atom is 5.293 10-13 m or 52.93 pm.An increase in the principal quantum number from n = 1 to n = corresponds to the ionization of the atom and the ionization energy, IE, quoted per mole of atoms.H(g) H+(g) + e-= 2.179 10-18 J = 1312 kJ mol-1

CHEM210/Chapter 1/2014/08WAVE MECHANICSde Broglie (1924) if light composed of particles and showed wave-like properties, the same should be true for electrons and other particles.Proposed wave-particle duality and stated that classical mechanics with the idea of wave-like properties could be combined to show that a particle with momentum, mv possesses an associated wave of wavelength, .THE UNCERTAINTY PRINCIPLEWAVE NATURE OF ELECTRONSIf an electron has wave-like properties, it becomes impossible to know both the momentum and position of the electron at the same instant in time.To overcome this problem, we use the probability of finding the electron in a given volume of space and this is determined from the function 2, where is the wavefunction.

CHEM210/Chapter 1/2014/09SCHRDINGER WAVE EQUATIONEquation may be represented in several forms, but the following equation is appropriate for motion in the x direction.where m = mass, E = total energy, V = potential energy of the particle.In reality, electrons move in 3-dimensional space, and an appropriate form of the equation is given by:Results of the wave equation:Wavefunction, is a solution of the Schrdinger equation and describes the behaviour of an electron in an atomic orbital.

CHEM210/Chapter 1/2014/10Can find energy values associated with particular wavefunctions.Quantization of energy levels arises naturally from the Schrdinger equation.ATOMIC ORBITALSTHE QUANTUM NUMBERS n, l and mlThe principal quantum number, n, is a positive integer with values lying between the limits 1 n ; arise when the radial part of the wavefunction is solved.Two more quantum numbers, l and ml , appear when the angular part of the wavefunction is solved. The quantum number l is called the orbital quantum number and has allowed values of 0, 1, 2, . , (n-1). Its value determines the shape of the atomic orbital and the orbital angular momentum of the electron.The value of the magnetic quantum number, ml , gives information about the directionality of an atomic orbital and has integral values between +l and l.

CHEM210/Chapter 1/2014/11SHELLS, SUBSHELLS AND ORBITALSAll orbitals with the same value of n have the same energy and are said to be degenerate.Therefore, n defines a series of shells of the atom or sets of orbitals with the same value of n, hence with the same energy and approximately the same radial extent.Shells with n = 1, 2, 3, . are commonly referred to as K, L, M, . shells. Orbitals belonging to each shell are classified into subshells distinguished by a quantum number l.For a given value of n, the quantum number l can have the values l = 0, 1, .. , n 1, e.g. the shell consists of just one subshell with l = 0, the shell with n = 2 consists of two subshells, one with l = 0 and the other with l = 1.Value of l01234 ..Subshell designationspdfg ..

CHEM210/Chapter 1/2014/12ELECTRON SPINTwo more quantum numbers required to specify the spatial distribution of an electron in an atom and are related to spin.Spin is described by two quantum numbers, s and ms.Spin magnetic quantum number, ms takes only two values, + and -NODESOrbitals are best expressed in terms of spherical polar coordinates.The positions where the wavefunction passes through zero are called nodes.There are two types of nodes, radial nodes occur where the radial component of the wavefunction passes through zero and angular nodes occur where the angular component of the wavefunction passes through zero.An orbital with quantum numbers n and l, in general has n l - 1 radial nodes.

CHEM210/Chapter 1/2014/13






CHEM210/Chapter 1/2014/19Relationship between quantum numbers and atomic orbitals.nlmlNo. of orbitalsAO designation10011s20012s1-1, 0, 132px, 2py, 2pz30013s1-1, 0, 133px, 3py, 3pz2-2,-1,0,1,253dxy, 3dyz, 3dzx, 3dx2- y2, 3dz2

An orbital is fully occupied when it contains two electrons which are spin-paired; one electron has a value of ms = + and the other, ms = -.Atomic orbitals are regions of space where the probability of finding an electron about an atom is highest.

CHEM210/Chapter 1/2014/20s orbitals are spherically symmetric.As n increases, the s orbitals get larger and the number of nodes increase.At a node, 2= 0 and for an s orbital, the number of nodes is (n-1).The s OrbitalsA node is a region in space where the probability of finding an electron is zero.

1s2s3s 4s


Height of graph indicates density of dots as we move from origin

CHEM210/Chapter 1/2014/22The p OrbitalsThere are three p-orbitals px, py, and pz which lie along the x-, y- and z- axes of a Cartesian system. Correspond to allowed values of ml of -1, 0, and +1.The orbitals are dumbbell shaped and as n increases, the p orbitals get larger.All p orbitals have a node at the nucleus.

pz px py pz px py

2p 3p



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Chapter 1 Atomic Structure