chapter 1: atomic structure

CHAPTER 1: ATOMIC STRUCTURE

CHEM210/Chapter 1/2014/01

An 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.


NUCLIDES, ATOMIC NUMBER AND MASS NUMBER

A 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.

E𝑍𝐴 element symbol

atomic number

mass number

RELATIVE ATOMIC MASSAtomic mass unit is defined as 1/12 of the mass of a atom.

Relative atomic masses (Ar) are all masses relative to = 12.0000.

ISOTOPESSame number of protons and electrons but different mass numbers.

ATOMIC NUMBER, MASS NUMBER AND ISOTOPES


EXAMPLECalculate the value of Ar for naturally occurring chlorine if the distribution of isotopes is 75.77% and 24.23% . Accurate masses for and are 34.97 and 36.97.

SOLUTIONThe relative atomic masses of chlorine is the weighted mean of the mass numbers of the two isotopes.

Ar = (75.77100

× 34.97)+ (24.23100

× 36.97) = 35.45

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?

Calculate the value of Ar for naturally occurring copper if the distribution of isotopes is 69.2% and 30.8% ; accurate masses are 62.93 and 64.93.


QUANTUM THEORY

Development 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 = Planck’s constant = 6.626 × 10-34 Js

∆ E = h ν = hcλ

One of the important applications of early quantum theory was the Rutherford- Bohr model of the hydrogen atom.


Balmer (1885) – wavelength of the spectral lines of hydrogen obeyed the equation:

𝜈=1𝜆=𝑅 ( 1

22 − 1𝑛2 )

where R is the Rydberg constant for hydrogen, is the wavenumber in cm-1 and n is an integer 3, 4, 5, …

The various series in atomic H emission spectrum

Series n″ n′ RegionLyman 1 2,3,4, …. UV Balmer 2 3,4,5, …. Visible Paschen 3 4,5,6, ….

IR Brackett 4 5,6,7, …. IR Pfund 5

6,7,8, …. IR

BOHR’S THEORY OF THE ATOMIC SPECTRUM OF HYDROGEN


Bohr (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:

𝑚𝑣𝑟=𝑛( h2𝜋 )

where m = mass of electron, v = velocity of electron, r = radius of the orbit and h = Planck constant

Energy is absorbed or emitted only when an electron moves from one stationary state to another and the energy change is given by:

∆𝐸=𝐸𝑛2−𝐸𝑛1

=h ν

where n1 and n2 are the principal quantum numbers.


If we apply the Bohr model to the hydrogen atom, the radius of each allowed circular orbit can be determined from the equation:

𝑟𝑛=𝜀𝑜h2𝑛2

𝜋𝑚𝑒𝑒2

where εo = permittivity of a vacuum = 8.854 10-12 F m-1

For 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-

𝐼𝐸=𝐸∞ −𝐸1=h𝑐λ =h𝑐𝑅 ( 1

12 − 1∞2 ) = 2.179 10-18 J = 1312 kJ mol-1


WAVE MECHANICS

de 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, λ.

λ= h𝑚𝑣

THE UNCERTAINTY PRINCIPLE

WAVE NATURE OF ELECTRONS

If 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 Ψ2, where Ψ is the wavefunction.


SCHRӦDINGER WAVE EQUATION

The Schrӧdinger equation can be solved exactly only for a species containing a nucleus and only one electron, e.g. 1H, i.e. hydrogen-like system.

Equation may be represented in several forms, but the following equation is appropriate for motion in the x direction.

Ψ = 0

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:

Ψ = 0

Results of the wave equation:

• Wavefunction, Ψ is a solution of the Schrӧdinger equation and describes the behaviour of an electron in an atomic orbital.


• Can find energy values associated with particular wavefunctions.

• Quantization of energy levels arises naturally from the Schrӧdinger equation.

ATOMIC ORBITALSTHE QUANTUM NUMBERS n, l and ml

The 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.


SHELLS, SUBSHELLS AND ORBITALS

All 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 l 0 1 2 3 4 …..Subshell designation s p d f g …..


ELECTRON SPIN

Two 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, +½ and -½

NODES

Orbitals 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.


Relationship between quantum numbers and atomic orbitals.

n l ml No. of orbitals AO designation

1 0 0 1 1s

2 0 0 1 2s

1 -1, 0, 1 3 2px, 2py, 2pz

3 0 0 1 3s

1 -1, 0, 1 3 3px, 3py, 3pz

2 -2,-1,0,1,2 5 3dxy, 3dyz, 3dzx,

3dx2

- y2, 3dz

2

An orbital is fully occupied when it contains two electrons which are spin-paired; one electron has a value of ms = +½ and the other, ms = -½.

Atomic orbitals are regions of space where the probability of finding an electron about an atom is highest.


s orbitals are spherically symmetric.As n increases, the s orbitals get larger and the number of nodes increase.

At a node, Ψ2= 0 and for an s orbital, the number of nodes is (n-1).

The s Orbitals

A node is a region in space where the probability of finding an electron is zero.

1s2s

3s

4s


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


The p Orbitals

There 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

http://en.wikipedia.org/wiki/File:P2M0.png


http://en.wikipedia.org/wiki/File:P2M-1.png



http://en.wikipedia.org/wiki/File:P3M-1.png

chapter 1: atomic structure

Documents