Atomic Structure and Periodicity - hsbr1.com 2 Atomic Structure and Periodicity. Chapter 2 Table of...

Chapter 2

Atomic Structureand Periodicity

Chapter 2Table of Contents

Copyright ©2016 Cengage Learning. All Rights Reserved.

(2.1) Electromagnetic radiation

(2.2) The nature of matter

(2.3) The atomic spectrum of hydrogen

(2.4) The Bohr model

(2.5) The quantum mechanical model of the atom

(2.6) Quantum numbers

(2.7) Orbital shapes and energies

(2.8) Electron spin and the Pauli principle

(2.9) Polyelectronic atoms

Chapter 2Table of Contents


(2.10) The history of the periodic table

(2.11) The aufbau principle and the periodic table

(2.12) Periodic trends in atomic properties

(2.13) The properties of a group: The alkali metals

Chapter 2


Questions to Consider

Why do we get colors?

Why do different chemicals give different colors?

Section 2.1Electromagnetic Radiation


Electromagnetic Radiation - Characteristics

One of the ways by which energy travels through space

Three characteristics:

Wavelength (λ) is the distance between two peaks or troughs in a wave

Frequency (ν) points to the number of waves (cycles) per second that pass a given point in space

Speed

The speed of light is 2.9979×108 m/s



Relationship between Wavelength and Frequency

There exists an inverse relationship between λ and ν

1/

or

=

λ

λ c

n

n

The way I remember this…

n=c/l



Figure 2.1 - The Nature of Waves



Figure 2.2 - Classification of Electromagnetic Radiation



Interactive Example 2.1 - Frequency of Electromagnetic Radiation

The brilliant red colors seen in fireworks are due to the emission of light with wavelengths around 650 nm when strontium salts such as Sr(NO3)2 and SrCO3 are heated. Calculate the frequency of red light of wavelength 6.50× 102

nm.

Solution

We can convert wavelength to frequency using the equation:

= or =c

λ cλ

n n



Interactive Example 2.1 - Frequency of Electromagnetic Radiation

Where c = 2.9979×108 m/s. In this case λ = 6.50 × 102 nm

Changing the wavelength to meters, we have

26.50×10 nm9

1m×

10 nm

7

8

= 6.50×10 m

and

2.9979×10 m= =

cν

λ

7

/ s

6.50×10 m

14 1 14= 4.61×10 s = 4.61×10 Hz



Pickle Light

On applying an alternating current of 110 volts to a dill pickle, a glowing discharge can be observed

The Na+ and Cl– ions in the forks cause the sodium atoms to get into an excited state

When the atoms reach their ground state, they emit visible light at 589 nm

Section 2.2The Nature of Matter


An Introduction

Max Planck observed that energy can be gained or lost only in whole-number multiples of hν

Where h is Planck's constant with a value of 6.626 ×10–34 J · s

The change in energy for a system ΔE can be represented by the equation , where

n is an integer

h is Planck’s constant

ν represents the frequency of electromagnetic radiation

ΔE = nhn



Quantized Energy

Planck also observed that energy can be quantized and can occur only in discrete units called quanta

A system can transfer energy only in whole quanta

This proves that energy does have particulate properties



Interactive Example 2.2 - The Energy of a Photon

The blue color in fireworks is often achieved by heating copper(I) chloride (CuCl) to about 1200°C. Then the compound emits blue light having a wavelength of 450 nm. What is the increment of energy (the quantum) that is emitted at 4.50 × 102 nm by CuCl?

Solution

The quantum of energy can be calculated from the equation:

ΔE = hn



Interactive Example 2.2 - The Energy of a Photon

The frequency ν for this case can be calculated as follows:

So,

A sample of CuCl emitting light at 450 nm can lose energy only in increments of 4.41×10–19 J, the size of the quantum in this case

82.9979×10 m= =

c

λn

7

/ s

4.50×10 m

14 1= 6.66×10 s

34Δ = = 6.626×10 J.sE hn 146.66×10 s 1 19= 4.41×10 J



The Concept of Photons

Electromagnetic radiation is a stream of “particles” called photons

The energy of each photon can be expressed by:

Where h is Planck’s constant, ν is the radiation frequency, and λis the radiation wavelength

photon = =hc

E hλ

n



The Photoelectric Effect

The phenomenon whereby electrons are emitted from the surface of a metal when light strikes it

Characteristics:

No electrons are emitted by any given metal below a specified threshold frequency, ν0

When ν < ν0 , no electrons are emitted, regardless of the intensity of light

When ν > ν0 , the number of electrons increases with the intensity of light

When ν > ν0 , the kinetic energy of emitted electrons increases linearly with the frequency of the light




Minimum energy required to remove an electron = E0 = hν0

When ν > ν0 , the excess energy that is required to remove the electron is given as kinetic energy (KE):

Where

m is the mass of the electron

v is the velocity of the electron

ν is the energy incident of the photon

ν0 is the energy required to expel the electron

2electron 0

1KE = =

2mv h hn n




Greater intensity of light means that more photons are available to release electrons, which gave rise to the equation:

The theory of relativity signifies that energy has mass

This equation can be used to calculate mass associated with a quantity of energy

The mass of a photon of light with wavelength λ is given by:

2E = mc

= = =2 2

E hc / λ hm

c c λc



Dual Nature of Light

The phenomenon whereby electromagnetic radiation (and all matter) exhibits wave properties and particulate properties

de Broglie’s equation allows for the calculation of the wavelength of a particle

hλ =

mv



Diffraction

It is the result of light getting scattered from a regular array of points or lines

This scattered radiation produces a diffraction pattern on bright and dark areas

Scattered light can:

Interfere constructively and produce a bright area

Interfere destructively to produce a dark spot

This phenomenon occurs best when the spacing between scattering points is similar to the wavelength of the diffracted wave



Figure 2.6 - A Diffraction Pattern of a Beryl Crystal

Section 2.3The Atomic Spectrum of Hydrogen


Significance of the Hydrogen Emission Spectrum

Continuous spectrum occurs when white light is passed through a prism

Contains all the wavelengths of visible light

Hydrogen emission spectrum is called a line spectrum

Displays only a few lines, each line corresponding to discrete wavelengths

Indicates that the energy of the electron on the hydrogen atom is quantized



Significance of the Hydrogen Emission Spectrum

Change in energy from a high to lower level of a given wavelength can be calculated by:

Δ = =hc

E hλ

n

Change in energy Frequency of light emitted

Wavelength of light emitted



Figure 2.7 - (a) Continuous Spectrum and (b) Line Spectrum



Concept Check

Why is it significant that the color emitted from the hydrogen emission spectrum is not white?

How does the emission spectrum support the idea of quantized energy levels?

Section 2.4The Bohr Model


Quantum Model for the Hydrogen Atom

Electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits

Bohr’s model gave the hydrogen atom energy levels consistent with the hydrogen emission spectrum

The expression for the energy levels available to the electron in the hydrogen atom can be expressed as:

Where n is an integer and Z is the nuclear charge

2182.178×10 J

2

ZE =

n



Figure 2.9 - Electronic Transitions in the Bohr Model for the Hydrogen Atom: Part (a)

(a) An energy-level diagram for the first three electronic transitions



Figure 2.9 - Electronic Transitions in the Bohr Model for the Hydrogen Atom: Part (b) and (c)

(b) An orbit-transition diagram, which accounts for the experimental spectrum

(c) The resulting line spectrum on a photographic plate




When the hydrogen atom returns to its lowest possible energy state, it is called the ground state

When the electron falls from n=6 to n=1, ΔE can be computed by:

The negative sign indicates that the atom has lost energy and is in a more stable state

18 201 6

18

ΔE = energy of final state energy of initial state

= = 2.178×10 J 6.050×10 J

= 2.117×10 J

E E




The energy lost is taken away from the atom by the emission of a photon whose wavelength can be calculated from:

ΔE, the change in energy of the atom, is equal to the energy of the emitted photon

Δ = or λ =Δ

c hcE h

λ E

34(6.626×10 J= =

Δ

hcλ

E

. s 8)(2.9979×10 m / s 18

)

2.117×10 J

8= 9.383×10 m



Interactive Example 2.4 - Energy Quantization in Hydrogen

Calculate the energy required to excite the hydrogen electron from level n = 1 to level n = 2. Also calculate the wavelength of light that must be absorbed by a hydrogen atom in its ground state to reach this excited state.

Solution

Using the equation with Z = 1, we have:2

182.178×10 J2

ZE =

n

218 18

1 2

218 19

2 2

1= 2.178×10 J = 2.178×10 J

1

1= 2.178×10 J = 5.445×10 J

2

E

E



Interactive Example 2.4 - Energy Quantization in Hydrogen

The positive value for ΔE indicates that the system has gained energy

The wavelength of light that must be absorbed to produce this change is:

19 18 18Δ = = 5.445 × 10 J 2.178 × 10 J = 1.633×10 J2 1E E E

34(6.626×10 J= =

Δ

hcλ

E

. s 8) (2.9979×10 m / s18

)

1.633×10 J

7= 1.216×10 m



Importance of the Bohr Model

The model correctly fits the quantized energy levels of the hydrogen atom

It postulates only certain allowed circular orbits for the electron

As the electron becomes more tightly bound, its energy becomes more negative relative to the free electron

The free electron is at infinite distance from the nucleus

As the electron is brought closer to the nucleus, energy is released from the system



Energy Change Between Levels in a Hydrogen Atom

The general equation for the electron moving from ninitial to nfinal can be derived by using the following equation:

2182.178×10 J

2

ZE =

n

final initial

final initial

2 218 18

2 2final initial

18

2 2final initial

Δ = energy of level energy of level

=

1 1 = ( 2.178×10 J) 2.178×10 J

1 1 = 2.178×10 J

E n n

E E

n n

n n



Drawbacks of the Bohr Model

This model only works for hydrogen

Electrons do not move around the nucleus in circular orbits

Section 2.5The Quantum Mechanical Model of the Atom


Erwin Schrödinger and Quantum Mechanics

Standing waves are stationary waves that do not travel along any length

Only certain orbits have a circumference into which whole number wavelengths of standing electron waves will fit

Other waves produce destructive interference of the standing electron wave

The mathematical representation for a standing wave is:

ˆ =H E



Erwin Schrödinger and Quantum Mechanics

ψ represents the wave function, which is a function of the coordinates of the electron’s position in 3-dimensional space

represents an operator

A specific wave function is termed as an orbital

Wave function does not provide information about the pathway of the electron

H



Heisenberg Uncertainty Principle

There is a fundamental limitation to just how precisely we can know both the position and momentum of a particle at a given time

Mathematically, this principle can be represented by:

Where

Δx is the uncertainty in a particle’s position

Δ(mν) is the uncertainty in a particle’s momentum

h is Planck’s constant

Δ . Δ( )4

hx mv



Physical Meaning of the Wave Function

The square of the function, represented as a probability distribution, indicates the probability of finding an electron near a particular point in space

The intensity of color is used to indicate the probability value near a given point in space

The more time the electron visits a particular point, the darker the negative becomes

This diagram is known as an electron density map



Figure 2.12 - Probability Distribution for the 1s Wave Function - Part (a) and (b)

(a) The probability distribution for the hydrogen 1s orbital in three-dimensional space

(b) The probability of finding the electron at points along a line drawn from the nucleus outward in any direction



Physical Meaning of a Wave Function

A radial probability distribution graph plots the total probability of finding an electron in each spherical shell versus the distance from the nucleus

Probability of finding an electron at a particular position is greatest near the nucleus

Volume of the spherical shell increases with distance from the nucleus

The size of the 1s orbital can be stated as the radius of the sphere that encloses 90% of the total electron probability



Figure 2.13 - Radial Probability Distribution

(a) Cross section of the hydrogen 1s orbital probability distribution divided into successive thin spherical shells

(b) Radial probability distribution plot

Section 2.6Quantum Numbers


An Introduction to Quantum Numbers They express the various properties of the orbital

Principal quantum number (n) has integral values and is related to the size and energy of the orbital

Angular momentum quantum number (l or l) has integral values from 0 to n – 1

It is related to the shape of atomic orbitals (sometimes called a subshell)

Magnetic quantum number (ml) has integral values +l to -l

It is related to the orientation of the orbital in space relative to the other orbitals in the atom

Electron spin quantum number (ms) can be + ½ or – ½

It means that the electron can spin in either of the two opposite directions









Interactive Example 2.6 - Electron Subshells

For principal quantum level n = 5, determine the number of allowed subshells (different values of l), and give the designation of each

Solution

For n = 5, the allowed values of l run from o to 4 (n – 1 = 5 – 1 )

Thus, the subshells and their designations are:

l = 0 l = 1 l = 2 l = 3 l = 4

5s 5p 5d 5f 5g

Section 2.7Orbital Shapes and Energies


An Introduction

Areas of zero probability are called nodal surfaces or nodes

The number of nodes increase as n increases

The number of nodes for the s orbital is given by n – 1



Figure 2.14 - Representations of the Hydrogen 1s, 2s, and 3s Orbitals



p Orbitals

Not spherical like s orbitals

Have two lobes separated by a node at the nucleus

Labelled as per the axis of the xyz coordinate system



The d Orbitals

Do not correspond to principal quantum levels n = 1 and n = 2

First level occur in level n = 3

They possess two fundamental shapes:

dxz , dyz , dxy , and dx2

– y2

Have four labels that are centered in the plane that appears in the orbital label

dz2

Possesses a unique shape with two lobes that run along the z axis and a belt centered in the xy plane

d orbitals, where n>3, appear as 3d orbitals and have larger lobes



Figure 2.17 - Representation of the 3d Orbitals - Part (b)

(b) The boundary surfaces of all five 3d orbitals, with the signs (phases) indicated



f Orbitals and Degenerates

The f orbitals first occur in level n = 4

These orbitals are not involved in bonding in any compounds

All orbitals with the same value of n have the same energy and are said to be degenerate

In the ground state, the single hydrogen electron can be found in the 1s orbital

This electron can be excited to higher-energy orbitals



Figure 2.18 - Representation of the 4f Orbitals in Terms of Their Boundary Surfaces

Section 2.8Electron Spin and the Pauli Principle


Electron Spin

Electron spin quantum number (ms) can be + ½ or – ½

It means that the electron can spin in either of the two opposite directions

Pauli exclusion principle states that in a given atom no two electrons can have the same set of four quantum numbers

An orbital can hold only two electrons, and they must have opposite spins because only two values of ms are allowed

Section 2.8Electron Spin and the Pauli Principle


Figure 2.20 - The Spinning Electron - Part (a) and (b)

• Spinning in one direction, the electron produces the magnetic field oriented as shown in (a)

• Spinning in the opposite direction, it gives a magnetic field of the opposite orientation, as shown in (b)

Section 2.9Polyelectronic Atoms


An Introduction

Polyelectronic atoms are those atoms with more than one electron

Electron correlation problem

Since the electron pathways are unknown, electron repulsions cannot be accurately calculated

When electrons are placed in a particular quantum level, the orbital levels vary in energy as follows:

Ens < Enp < End < Enf





The Penetration Effect

A 2s electron on average is closer to the nucleus (penetration) than one in the 2p orbital

This causes an electron in a 2s orbital to be attracted to the nucleus more strongly than an electron in a 2p orbital

The 2s orbital is lower in energy than the 2p orbitals in a polyelectronic atom

The same occurrence can be noticed in other quantum levels



Figure 2.22 - Part (b) The Radial Probability Distribution for the 3s, 3p, and 3d orbitals

Section 2.10The History of the Periodic Table


The periodic table was originally constructed to represent the patterns observed in the chemical properties of elements

Mendeleev’s periodic table:

Emphasized on how the table could help estimate the existence and properties of unkown elements

Rectified several values of atomic masses

The current periodic table lists elements by their atomic number rather than atomic mass

Section 2.11The Aufbau Principle and the Periodic Table


Aufbau Principle

As protons are added one by one to the nucleus to build up the elements, electrons are similarly added to hydrogen-like orbitals

Example - An oxygen atom has an electron arrangement of two electrons in the 1s subshell, two electrons in the 2s subshell, and four electrons in the 2p subshell



Orbital Diagrams

They represent the number of electrons an atom has in each of its occupied orbitals

Example - The orbital diagram of oxygen:

O: 1s22s22p4 1s 2s 2p





Hund’s Rule

The rule states that the lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli principle in a particular set of degenerate orbitals

Unpaired electrons are represented as having parallel spins

Example - The orbital diagram for neon:

Ne: 1s22s22p6 1s 2s 2p



Valence Electrons

They are electrons in the outermost principal quantum level of an atom

Example - For the sodium atom, the valence electron is that in the 3s orbital

Inner electrons are termed core electrons

The elements in the same group on the periodic table have the same valence electron configuration and display similar chemical behavior





Groups in the Periodic Table

Transition metals are those whose configuration is obtained by adding electrons to the five 3d orbitals

The configuration for chromium is:

Cr: [Ar]4s13d 5

After lanthanum, the lanthanide series occurs, which corresponds to the filling of the seven 4f orbitals

The actinide series corresponds to the filling of the seven 5f orbitals



Main-Group or Representative Elements

The labels for Groups 1A, 2A, 3A, 4A, 5A, 6A, 7A, and 8A indicate the total number of valence electrons

Each member of these groups has the same valence electron configuration



Figure 2.29 - The Orbitals Being Filled for Elements in Various Parts of the Periodic Table



Interactive Example 2.7 - Electron Configurations

Give the electron configurations for sulfur (S) and cadmium (Cd)

Solution

Sulfur is element 16 and resides in Period 3, where the 3p orbitals are being filled

Since sulfur is the fourth among the “3p elements,” it must have four 3p electrons

Its configuration is:

S: 1s22s22p63s23p4 or [Ne]3s23p4





Interactive Example 2.7 - Electron Configurations

Cadmium is element 48 and is located in Period 5 at the end of the 4d transition metals

It is the tenth element in the series and thus has 10 electrons in the 4d orbitals, in addition to the 2 electrons in the 5s orbital

The configuration is:

Cd: 1s22s22p63s23p64s23d104p65s24d10 or [Kr]5s24d10

Section 2.12Periodic Trends in Atomic Properties


Commonly Observed Periodic Trends

Atomic radius

Ionization energy

Electron affinity



Atomic Radius

Atomic radii can be obtained by measuring the distance between atoms in chemical compounds

They are also called covalent atomic radii due to the manner in which they are determined

Since nonmetallic atoms do not form diatomic molecules, atomic radii are estimated from their covalent compounds

Metallic radii are obtained by calculating half the distance between metal atoms in solid metal crystals



Atomic Radii Trends

The atomic radius decreases in going across a period from left to right

Effective nuclear charge increases

Valence electrons are drawn closer to the nucleus, decreasing the size of the atom

Atomic radius increases in going down a group

Orbital sizes increase in successive principal quantum levels



Interactive Example 2.8 - Trends in Radii

Predict the trend in radius for the following ions:Be2+, Mg2+, Ca2+, and Sr2+

Solution

All these ions are formed by removing two electrons from an atom of a Group 2A element

In going from beryllium to strontium, we are going down the group, so the sizes increase:

Be2+ < Mg2+ < Ca2+ < Sr2+

↑ ↑

Smallest radius Largest radius





Ionization Energy

It refers to the energy required to remove an electron from a gaseous atom or ion

The atom or ion is assumed to be in its ground state

The energy required to remove the highest-energy electron of an atom is called the first ionization energy (I1)

The value of I1 is generally smaller than that of I2, which is the second ionization energy

+( ) ( )X X + eg g



Ionization Energy Trends in the Periodic Table

While going across a period from left to right, the first ionization energy increases

Electrons added to the same principal quantum level cannot completely shield the increasing nuclear charge and are generally more strongly bound from left to right on the periodic table

While going down a group from top to bottom, the first ionization energy decreases

The electrons being removed are farther from the nucleus



Figure 2.34 - The Values of First Ionization Energy for the Elements in the First Six Periods



Interactive Example 2.10 - Ionization Energies

Consider atoms with the following electron configurations:

1s22s22p6

1s22s22p63s1

1s22s22p63s2

Which atom has the largest first ionization energy, and which one has the smallest second ionization energy? Explain your choices.




Solution

The atom with the largest value of l1 is the one with the configuration 1s22s22p6 (this is the neon atom), because this element is found at the right end of Period 2

Since the 2p electrons do not shield each other very effectively, l1 will be relatively large

The other configurations given include 3s electrons, which are effectively shielded by the core electrons and are farther from the nucleus than the 2p electrons in neon

Thus l1 for these atoms will be smaller than for neon




The atom with the smallest value of l2 is the one with the configuration 1s22s22p63s2 (the magnesium atom)

For magnesium, both l1 and l2 involve valence electrons

For the atom with the configuration 1s22s22p63s1 (sodium), the second electron lost (corresponding to l2) is a core electron (from a 2p orbital)



Electron Affinity

It refers to the energy change associated with the addition of an electron to a gaseous atom

While going across a period from left to right, electron affinities become more negative

Electron affinity becomes more positive in going down a group

Electrons are added at increasing distances from the nucleus

– –X + e) ( )X(g g



Concept Check

Explain why the graph of ionization energy versus atomic number (across a row) is not linear.

Where are the exceptions?



Concept Check

Which of the following would require more energy to remove an electron?

Why?

Na Cl





Concept Check

Which of the following would require more energy to remove an electron?

Why?

Li Cs



Concept Check

Which element has the larger second ionization energy?

Why?

Lithium Beryllium





Concept Check

Which of the following should be the larger atom?

Why?

Na Cl



Concept Check

Which of the following should be the larger atom?

Why?

Li Cs





Concept Check

Which is larger?

The hydrogen 1s orbital

The lithium 1s orbital

Which is lower in energy?

The hydrogen 1s orbital

The lithium 1s orbital

Section 2.13The Properties of a Group: The Alkali Metals


Information in the Periodic Table

The number and type of valence electrons primarily determine the chemistry of an atom

Electron configurations can be determined from the organization of the periodic table

Certain groups in the periodic table have special names

Elements in the periodic table are basically divided into metals and nonmetals

Elements that exhibit both metallic and nonmetallic properties are termed metalloids of semimetals



Figure 2.37 - Special Names for Groups in the Periodic Table





Figure 2.37 - Special Names for Groups in the Periodic Table (Contd.)



The Alkali Metals

Li, Na, K, Rb, Cs, and Fr are the most chemically reactive of the metals

Hydrogen exhibits a nonmetallic character due to its small size

Going down a group:

Ionization energy decreases

Atomic radius increases

Density increases

Melting and boiling points decreases smoothly

Date post:	10-May-2018
Category:	Documents
Upload:	nguyenkhanh
View:	224 times
Download:	0 times

Atomic Structure and Periodicity - hsbr1.com 2 Atomic Structure and Periodicity. Chapter 2 Table of...

Documents