electronic structure of atoms chapter 6 electronic structure of atoms dr. subhash c. goel south ga...

ElectronicStructureof Atoms

Chapter 6

Electronic Structure of Atoms

Dr. Subhash C. Goel

South GA College

Douglas, GA

Copyright © Cengage Learning. All rights reserved. 7 | 2

A wave is a continuously repeating change or oscillation in matter or in a physical field.

Light is an electromagnetic wave, consisting of oscillations in electric and magnetic fields traveling through space.


A wave can be characterized by its wavelength and frequency.

Wavelength, symbolized by the Greek letter lambda, , is the distance between any two identical points on adjacent waves.


Frequency, symbolized by the Greek letter nu, , is the number of wavelengths that pass a fixed point in one unit of time (usually a second). The unit is 1/S or s-1, which is also called the Hertz (Hz).


Wavelength and frequency are related by the wave speed. The speed of light, c, is 3.00 x 108 m/s.

c =

The relationship between wavelength and frequency due to the constant velocity of light is illustrated on the next slide.


When the wavelength is reduced by a factor of two, the frequency increases by a factor of two.

Exercise:1. What is the wavelength of blue light with a frequency of 6.4 1014/s?

2. What is the frequency of light having a wavelength of 681 nm?



The range of frequencies and wavelengths of electromagnetic radiation is called the electromagnetic spectrum.


© 2012 Pearson Education, Inc.

The Nature of EnergyThe wave nature of light does not explain how an object can glow when its temperature increases.

Also, The wave theory could not explain the photoelectric effect.



The Nature of Energy

Max Planck explained it by assuming that energy comes in packets called quanta.




• Einstein used this assumption to explain the photoelectric effect.

• He concluded that energy is proportional to frequency:

E = hwhere h is Planck’s constant, 6.626 10−34 J-s.




• Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light:

c = E = h

© 2012 Pearson Education, Inc.Chemistry, The Central Science, 12th EditionTheodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward

Exercise Energy of a Photon

Calculate the energy of one photon of yellow light that has a wavelength of 589 nm.


In the early 1900s, the atom was understood to consist of a positive nucleus around which electrons move (Rutherford’s model).

This explanation left a theoretical dilemma: According to the physics of the time, an electrically charged particle circling a center would continually lose energy as electromagnetic radiation. But this is not the case—atoms are stable.


In addition, this understanding could not explain the observation of line spectra of atoms.

A continuous spectrum contains all wavelengths of light.

A line spectrum shows only certain colors or specific wavelengths of light. When atoms are heated, they emit light. This process produces a line spectrum that is specific to that atom. The emission spectra of six elements are shown on the next slide.


Emission of Energy(2 Possibilities)

Continuous Energy Loss Quantized Energy Loss

or


Emission of Energy

Continuous Energy Loss

• Any and all energy values possible on way down

• Implies electron can be anywhere about nucleus of atom

Continuous emission spectra

Quantized Energy Loss

• Only certain, restricted, quantized energy values possible on way down

• Implies an electron is restricted to quantized energy levels

Line spectra


7.3

Line Emission Spectrum of Hydrogen Atoms


Line Spectra vs. Continuous Emission Spectra

• The fact that the emission spectra of H2 gas and other molecules is a line rather than a continuous emission spectra tells us that electrons are in quantized energy levels rather than anywhere about nucleus of atom.


In 1913, Neils Bohr, a Danish scientist, set down postulates to account for

1. The stability of the hydrogen atom

2. The line spectrum of the atom


Energy-Level Postulate

An electron can have only certain energy values, called energy levels. Energy levels are quantized.

For an electron in a hydrogen atom, the energy is given by the following equation:

RH = 2.179 10−18 J

n = principal quantum number

2H

n

RE


Transitions Between Energy LevelsAn electron can change energy levels by absorbing energy to move to a higher energy level or by emitting energy to move to a lower energy level.


For a hydrogen electron, the energy change is given by

2i

2f

H

11Δ

nnRE

ifΔ EEE

RH = 2.179 10−18 J, Rydberg constant


The energy of the emitted or absorbed photon is related to E:

We can now combine these two equations:

2i

2f

H

11

nnRh

constant sPlanck'

Δ electron

h

hEEphoton


Light is absorbed by an atom when the electron transition is from lower n to higher n (nf > ni). In this case, E will be positive.

Light is emitted from an atom when the electron transition is from higher n to lower n (nf < ni). In this case, E will be negative.

An electron is ejected when nf = ∞.


Ephoton = E = Ef - Ei

Ef = -RH ( )1n2

f

Ei = -RH ( )1n2

i

i fE = RH( )

1n2

1n2

nf = 1

ni = 2

nf = 1

ni = 3

nf = 2

ni = 3

7.3



Exercise: Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5

state to the n = 3 state.




• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:1. Electrons in an atom can only occupy certain orbits

(corresponding to certain energies)

2. Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.

2. Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by

E = h


In 1923, Louis de Broglie, a French physicist, reasoned that particles (matter) might also have wave properties.

The wavelength of a particle of mass, m (kg), and velocity, v (m/s), is given by the de Broglie relation:

34

λ

6.626 10 J s

h

mv

h


Building on de Broglie’s work, in 1926, Erwin Schrödinger devised a theory that could be used to explain the wave properties of electrons in atoms and molecules.

The branch of physics that mathematically describes the wave properties of submicroscopic particles is called quantum mechanics or wave mechanics.


Quantum mechanics alters how we think about the motion of particles.

In 1927, Werner Heisenberg showed how it is impossible to know with absolute precision both the position, x, and the momentum, p, of a particle such as electron.

Because p = mv this uncertainty becomes more significant as the mass of the particle becomes smaller.

4π))(Δ(Δ

hpx



Quantum Mechanics• The wave equation is

designated with a lowercase Greek psi (). No direct physical meaning.

• The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.



Quantum Numbers

• Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies.

• Each orbital describes a spatial distribution of electron density.

• An orbital is described by a set of three quantum numbers.



Principal Quantum Number (n)

• The principal quantum number, n, describes the energy level on which the orbital resides.

• The values of n are integers ≥ 1.

• For Hydrogen atom:

En= -(2.18X10-18)(1/n2) as in Bohr Model



Angular Momentum Quantum Number (l)

• This quantum number defines the shape of the orbital.

• Allowed values of l are integers ranging from 0 to n − 1.

• We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.



Angular Momentum Quantum Number (l)

Value of l 0 1 2 3

Type of orbital s p d f



Magnetic Quantum Number (ml)

• The magnetic quantum number describes the three-dimensional orientation of the orbital.

• Allowed values of ml are integers ranging from −l to l:

−l ≤ ml ≤ l

• Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, and so forth.



Magnetic Quantum Number (ml)

• Orbitals with the same value of n form a shell.• Different orbital types within a shell are subshells.



s Orbitals

• The value of l for s orbitals is 0.• They are spherical in shape.• The radius of the sphere increases with the

value of n.



s Orbitals

Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n − 1 nodes, or regions where there is 0 probability of finding an electron.



p Orbitals

• The value of l for p orbitals is 1.• They have two lobes with a node between

them.



d Orbitals

• The value of l for a d orbital is 2.

• Four of the five d orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.



Energies of Orbitals

• For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.

• That is, they are degenerate.



Energies of Orbitals

• As the number of electrons increases, though, so does the repulsion between them.

• Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate.



Spin Quantum Number, ms

• In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy.

• The “spin” of an electron describes its magnetic field, which affects its energy.



Spin Quantum Number, ms

• This led to a fourth quantum number, the spin quantum number, ms.

• The spin quantum number has only 2 allowed values: +1/2 and −1/2.


An electron configuration of an atom is a particular distribution of electrons among available subshells.

An orbital diagram of an atom shows how the orbitals of a subshell are occupied by electrons. Orbitals are represented with a circle or squares; electrons are represented with arrows up for ms= +½ or down for ms= -½.


The Pauli exclusion principle summarizes experimental observations that no two electrons in one atom can have the same four quantum numbers.

That means that within one orbital, electrons must have opposite spin. It also means that one orbital can hold a maximum of two electrons (with opposite spin).


An s subshell, with one orbital, can hold a maximum of 2 electrons.

A p subshell, with three orbitals, can hold a maximum of 6 electrons.

A d subshell, with five orbitals, can hold a maximum of 10 electrons.

An f subshell, with seven orbitals, can hold a maximum of 14 electrons.


In 1927, Friedrich Hund discovered, by experiment, a rule for determining the lowest-energy configuration of electrons in orbitals of a subshell.

Hund’s rule states that the lowest-energy arrangement of electrons in a subshell is obtained by putting electrons into separate orbitals of the subshell with the same spin before pairing electrons.


The lowest-energy configuration of an atom is called its ground state.

Any other allowed configuration represents an excited state.


The building-up principle (or aufbau principle) is a scheme used to reproduce the ground-state electron configurations by successively filling subshells with electrons in a specific order (the building-up order).

This order generally corresponds to filling the orbitals from lowest to highest energy. Note that these energies are the total energy of the atom rather than the energy of the subshells alone.


1s

2s 2p

3s 3p 3d

4s 4p 4d4f

5s 5p 5d5f

6s 6p 6d

7s 7p


This results in the following order:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p


Another way to learn the building-up order is to correlate each subshell with a position on the periodic table.

The principal quantum number, n, correlates with the period number.

Groups IA and IIA correspond to the s subshell; Groups IIIA through VIIIA correspond to the p subshell; the “B” groups correspond to the d subshell; and the bottom two rows correspond to the f subshell. This is shown on the next slide.


There are a few exceptions to the building-up order prediction for the ground state.

Chromium (Z=24) and copper (Z=29) have been found by experiment to have the following ground-state electron configurations:

Cr: 1s2 2s2 2p6 3s2 3p6 3d5 4s1

Cu: 1s2 2s2 2p6 3s2 3p6 3d10 4s1

In each case, the difference is in the 3d and 4s subshells.


There are several terms describing electron configurations that are important.

The complete electron configuration shows every subshell explicitly.

Br: 1s2 4p52s2 2p6 3s2 3p6 4s23d10


The noble-gas configuration substitutes the preceding noble gas for the core configuration and explicitly shows subshells beyond that.

Br: [Ar]3d104s24p5


The valence configuration consists of the electrons outside the noble-gas or pseudo-noble-gas core.

Br: 4s24p5


For main-group (representative) elements, an s or a p subshell is being filled.

For d-block transition elements, a d subshell is being filled.

For f-block transition elements, an f subshell is being filled.

?


Write the complete electron configuration of the arsenic atom, As, using the building-up principle.

1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p3

For arsenic, As, Z = 33.

?


What are the electron configurations for the valence electrons of arsenic and zinc?

Arsenic is in period 4, Group VA.Its valence configuration is 4s24p3.

Zinc, Z = 30, is a transition metal in the first transition series. Its noble-gas core is Ar, Z = 18.Its valence configuration is 4s23d10.


For nitrogen, the orbital diagram would be

1s 2s 2p

?


Write an orbital diagram for the ground state of the nickel atom.

3s 3p

1s 2s 2p

4s 3d

For nickel, Z = 28.


Magnetic Properties of Atoms

Although an electron behaves like a tiny magnet, two electrons that are opposite in spin cancel each other. Only atoms with unpaired electrons exhibit magnetic susceptibility.

This allows us to classify atoms based on their behavior in a magnetic field.


A paramagnetic substance is one that is weakly attracted by a magnetic field, usually as the result of unpaired electrons.

A diamagnetic substance is not attracted by a magnetic field generally because it has only paired electrons.

electronic structure of atoms chapter 6 electronic structure of atoms dr. subhash c. goel south ga...

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