chapter 5 models of the atom vanessa n. prasad-permaul valencia college chm1025 chapter 5 1 © 2011...

Chapter 5

Models ofthe Atom

Vanessa N. Prasad-Permaul

Valencia College

CHM1025

Chapter 5 1© 2011 Pearson Education, Inc.

Dalton Model of the Atom

John Dalton proposed that all matter is made up of tiny particles.

These particles are molecules or atoms.

Molecules can be broken down into atoms by chemical processes.

Atoms cannot be broken down by chemical or physical processes.

© 2011 Pearson Education, Inc.Chapter 5 2

Dalton Model

According to the law of definite composition, the mass ratio of carbon to oxygen in carbon dioxide is always the same. Carbon dioxide is composed of one carbon atom and two oxygen atoms.

Similarly, two atoms of hydrogen and one atom of oxygen combine to give water.

Dalton proposed that two hydrogen atoms could substitute for each oxygen atom in carbon dioxide to make methane with one carbon atom and four hydrogen atoms. Indeed, methane is CH4!


Dalton Atomic Theory

A Summary of Dalton Atomic Theory:

An element is composed of tiny, indivisible, indestructible particles called atoms.

1. All atoms of an element are identical and have the same properties.

2. Atoms of different elements combine to form compounds.

3. Compounds contain atoms in small whole number ratios.

4. Atoms can combine in more than one ratio to form different compounds.


Dalton Atomic Theory, Continued

The first two parts of atomic theory were later proven incorrect. We will see this later.

Proposals 3, 4, and 5 are still accepted today.

The Dalton theory was an important step in the further development of atomic theory.


Subatomic Particles

About 50 years after Dalton’s proposal, evidence was seen that atoms were divisible.

Two subatomic particles were discovered.

1. Negatively charged electrons, e–.

2. Positively charged protons, p+.

An electron has a relative charge of -1, and a proton has a relative charge of +1.


Thomson Model of the Atom

J. J. Thomson proposed a subatomic model of the atom in 1903.

Thomson proposed that the electrons were

distributed evenly throughout a

homogeneous sphere of positive charge.

This was called the plum pudding model

of the atom.© 2011 Pearson Education, Inc.Chapter 5 7

Mass of Subatomic Particles

Originally, Thomson could only calculate the mass-to-charge ratio of a proton and an electron.

Robert Millikan determined the charge of an electron in 1911.

Thomson calculated the masses of a proton and electron: An electron has a mass of 9.11 × 10-28 g.

A proton has a mass of 1.67 × 10-24 g.


Types of Radiation There are three types of radiation:

1. Alpha ()

2. Beta ()

3. Gamma ()

Alpha rays are composed of helium atoms stripped of their electrons (helium nuclei).

Beta rays are composed of electrons. Gamma rays are high-energy

electromagnetic radiation.


Rutherford Gold Foil Experiment

Rutherford’s student fired alpha particles at thin gold foils. If the plum pudding model of the atom was correct, α particles should pass through undeflected.

However, some of the alpha particles were deflected backward.


Explanation of Scattering Most of the alpha particles passed through

the foil because an atom is largely empty space.

At the center of an atom is the atomic nucleus, which contains the atom’s protons.

The alpha particles that bounced backward did did so after striking the dense nucleus.


Rutherford Model of the Atom Rutherford proposed a new model of the

atom:The negatively charged electrons are distributed around a positively charged nucleus.

An atom has a diameter of about 1 × 10-8 cm and the nucleus has a diameter of about 1 × 10-13 cm.

If an atom were the size of the Astrodome, the

nucleus would be the size of a marble.


Subatomic Particles Revisited Based on the heaviness of the

nucleus, Rutherford predicted that it must contain neutral particles in addition to protons.

Neutrons, n0, were discovered about 30 years later. A neutron is about the size of a proton without any charge.


Atomic Notation

Each element has a characteristic number of protons in the nucleus. This is the atomic number, Z.

The total number of protons and neutrons in the nucleus of an atom is the mass number, A.

We use atomic notation to display the number of protons and neutrons in the nucleus of an atom:


Sy symbol of the element

mass number (p+ and n0)

atomic number (p+)

AZ

Using Atomic Notation An example: Si

The element is silicon (symbol Si).

The atomic number is 14; silicon has 14 protons.

The mass number is 29; the atom of silicon has 29 protons + neutrons.

The number of neutrons is A – Z = 29 – 14 = 15 neutrons.


29

14

Example 5.1 Atomic Notation

We can draw a diagram of an atom by showing protons and neutrons in the nucleus surrounded by electrons.(a) Since the atomic number is 9 and the mass number is 19, the number of neutrons is 10 (19 – 9). If there are 9 protons, there must be 9 electrons.

Solution

Given the atomic notation for the following atoms, draw a diagram showing the arrangement of protons, neutrons, and electrons.

(a) (b)

(b) Since the atomic number is 47 and the mass number is 109, the number of neutrons is 62 (109 – 47). If there are 47 protons, there must be 47 electrons.

Exercise 5.1 Atomic Notation

Given the following diagram, indicate the nucleus using atomic notation.

Practice Exercise

Can atoms of different elements have the same atomic number?

Concept Exercise

Isotopes

All atoms of the same element have the same number of protons.

Most elements occur naturally with varying numbers of neutrons.

Atoms of the same element that have a different number of neutrons in the nucleus are called isotopes.

Isotopes have the same atomic number, but different mass numbers.


Isotopes, Continued We often refer to an isotope by

stating the name of the element followed by the mass number. Cobalt-60 is Carbon-14 is

How many protons and neutrons does an atom of lead-206 have? The atomic number of Pb is 82, so it has

82 protons. Pb-206 has 206 – 82 = 124 neutrons.


Co6037

C14 6

Example 5.2 Nuclear Composition of Isotopes

The subscript value refers to the atomic number (p+), and the superscript value refers to the mass number (p+ and n0).

(a)Thus, has 17 p+ and 20 n0 (37 – 17 = 20).

(b) In the periodic table, we find that the atomic number of mercury is 80. Thus, the atomic notation, , indicates 80 p+ and 122 n0 (202 – 80 = 122).

Solution

State the number of protons and the number of neutrons in an atom of each of the following isotopes.

(a) (b) mercury-202

Exercise 5.2 Nuclear Composition of Isotopes

State the number of protons and the number of neutrons in an atom of each of the following isotopes.

(a) (b) uranium-238

Practice Exercise

Can atoms of different elements have the same mass number?

Concept Exercise

Simple and Weighted Averages A simple average assumes the

same number of each object.

A weighted average takes into account the fact that we do not have equal numbers of all the objects.

A weighted average is calculated by multiplying the percentage of the object (as a decimal number) by its mass for each object and adding the numbers together.


Average Atomic Mass Since not all isotopes of an atom are

present in equal proportions, we must use the weighted average.

Copper has two isotopes:1. 63Cu, with a mass of 62.930 amu and

69.09% abundance.2. 65Cu, with a mass of 64.928 amu and

30.91% abundance.

The average atomic mass of copper is:

(62.930 amu)(0.6909) + (64.928amu)(0.3091) = 63.55 amu


Example 5.3 Calculation of Atomic Mass

We can find the atomic mass of silicon as follows:28Si: 27.977 amu 0.9221 = 25.80 amu29Si: 28.976 amu 0.0470 = 1.36 amu 30Si: 29.974 amu 0.0309 = 0.926 amu 28.09 amu

Solution

Silicon is the second most abundant element in Earth’s crust. Calculate the atomic mass of silicon given the following data for its three natural isotopes:

Exercise 5.3 Calculation of Atomic Mass

Calculate the atomic mass of copper given the following data:

Practice Exercise

A bag of marbles has 75 large marbles with a mass of 2.00 g each, and 25 small marbles with a mass of 1.00 g each. Calculate (a) the simple average mass, and (b) the weighted average mass of the marble collection.

Concept Exercise

Periodic Table We can use the periodic table to obtain the

atomic number and atomic mass of an element.

The periodic table shows the atomic number, symbol, and atomic mass for each element.


Example 5.4 Nuclear Composition from the Periodic Table

In the periodic table we observe

Solution

Refer to the periodic table on the inside cover of this textbook and determine the atomic number and atomic mass for iron.

The atomic number of iron is 26, and the atomic mass is 55.85 amu. From the periodic table information, we should note that it is not possible to determine the number of isotopes for iron or their mass numbers.

Exercise 5.4 Nuclear Composition from the Periodic Table

Which of the following is never a whole number value: atomic number, atomicmass, or mass number?

Concept Exercise

Refer to the periodic table on the inside cover of this text and determine the atomic number and mass number for the given radioactive isotope of radon gas.

Practice Exercise

Wave Nature of Light

Light travels through space as a wave, similar to an ocean wave. Wavelength is the distance light travels

in one cycle.

Frequency is the number of wave cycles completed each second.

Light travels at a constant speed: 3.00 × 108 m/s (given the symbol c).


Wavelength Versus Frequency The longer the wavelength of light, the

lower the frequency.

The shorter the wavelength of light, the higher the frequency.


Radiant Energy Spectrum The complete radiant energy

spectrum is an uninterrupted band, or continuous spectrum.

The radiant energy spectrum includes many types of radiation, most of which are invisible to the human eye.


Visible Spectrum

Light usually refers to radiant energy that is visible to the human eye.

The visible spectrum is the range of wavelengths between 400 and 700 nm.

Radiant energy that has a wavelength lower than 400 nm and greater than 700 nm cannot be seen by the human eye.


Example 5.5 Properties of Light

Referring to Figure 5.9, we notice that the wavelength of yellow light is about 600 nm and that of blue light is about 500 nm. Thus,

(a) yellow light has a longer wavelength than blue light.(b) blue light has a higher frequency because it has a shorter wavelength.(c) blue light has a higher energy because it has a higher frequency.

Solution

Considering blue light and yellow light, which has the(a) longer wavelength? (b) higher frequency?(c) higher energy?

Exercise 5.5 Properties of Light

Considering infrared light and ultraviolet light, which has the(a) longer wavelength? (b) higher frequency?(c) higher energy?

Practice Exercise

The energy of light (increases/decreases) as the wavelength increases. The energy of light (increases/decreases) as the frequency increases.

Concept Exercise

The Quantum Concept The quantum concept states that energy

is present in small, discrete bundles. For example:

A tennis ball that rolls down a ramp loses potential energy continuously.

A tennis ball that rolls down a staircase loses potential energy in small bundles. The loss is quantized.


Bohr Model of the Atom Niels Bohr speculated that electrons

orbit about the nucleus in fixed energy levels.

Electrons are found only in specific energy levels, and nowhere else.

The electron energy levels are quantized.


Example 5.6 Quantum Concept

Refer to Figure 2.3 if you have not used these balances in the laboratory.

(a)On a triple-beam balance a small metal rider is moved along a beam. Since the metal rider can be moved to any position on the beam, a triple-beam balance gives a continuous mass measurement.

(b) On a digital electronic balance the display indicates the mass of an object to a particular decimal place, for example, 5.015 g. Since the last digit in the display must be a whole number, a digital balance gives a quantized mass measurement.

Solution

State whether each of the following scientific instruments gives a continuous or a quantized measurement of mass:

(a)triple-beam balance(b) digital electronic balance

Figure 2.3 Balances for Measuring Mass (a) A platform balance having an uncertainty of ±0.1 g. (b) A beam balance having an uncertainty of ±0.01 g. (c) A digital electronic balance having an uncertainty of ±0.001 g.

Exercise 5.6 Quantum Concept

State whether each of the following musical instruments produces continuous or quantized musical notes:(a) acoustic guitar (b) electronic keyboard

Practice Exercise

Figure 2.3 Balances for Measuring Mass (a) A platform balance having an uncertainty of ±0.1 g. (b) A beam balance having an uncertainty of ±0.01 g. (c) A digital electronic balance having an uncertainty of ±0.001 g.

Complete the following quantum analogy: a water wave is to a drop of water, as a light wave is to a _______.

Concept Exercise

Emission Line Spectra When an electrical voltage is passed across a

gas in a sealed tube, a series of narrow lines is seen.

These lines are the emission line spectrum. The emission line spectrum for hydrogen gas shows three lines: 434 nm, 486 nm, and 656 nm.


Evidence for Energy Levels Bohr realized that this was the evidence

he needed to prove his theory.

The electric charge temporarily excites an electron to a higher orbit. When the electron drops back down, a photon is given off.

The red line is the least energetic and corresponds to an electron dropping from energy level 3

to energy level 2.


“Atomic Fingerprints” The emission line spectrum of each

element is unique.

We can use the line spectrum to identify elements using their “atomic fingerprint.”


Example 5.7 Emission Spectra and Energy Levels

When an electron drops from a higher to a lower energy level, light is emitted. For each electron that drops, a single photon of light energy is emitted. The energy lost by the electron that drops equals the energy of the photon that is emitted. Several photons of light having the same energy are observed as a spectral line.

Solution

Explain the relationship between an observed emission line in a spectrum and electron energy levels.

Exercise 5.7 Emission Spectra and Energy Levels

Indicate the number and color of the photons emitted for each of the following electron transitions in hydrogen atoms:(a) 1 e– dropping from energy level 3 to 2(b) 10 e– dropping from energy level 3 to 2(c) 100 e– dropping from energy level 4 to 2(d) 500 e– dropping from energy level 5 to 2

Practice Exercise

Which of the following statements are true according to the Bohr model of the atom?

(a) Electrons are attracted to the atomic nucleus.(b) Electrons have fixed energy as they circle the nucleus.(c) Electrons lose energy as they drop to an orbit closer to the nucleus.

Concept Exercise

Critical Thinking:“Neon Lights” Most “neon” signs don’t actually contain neon gas.

True neon signs are red in color. Each noble gas has its own emission spectrum,

and signs made with each have a different color.


Energy Levels and Sublevels It was later shown that electrons

occupy energy sublevels within each level.

These sublevels are given the designations s, p, d, and f. These designations are in reference to the

sharp, principal, diffuse, and fine lines in emission spectra.

The number of sublevels in each level is the same as the number of the main level.


Energy Levels and Sublevels, Continued

The first energy level has one sublevel designated 1s.

The second energy level has two sublevels designated 2s and 2p.

The third energy level has three sublevels designated 3s, 3p, and 3d.


Electron Occupancy in Sublevels

The maximum number of electrons in each of the energy sublevels depends on the sublevel: The s sublevel holds a maximum of 2 electrons. The p sublevel holds a maximum of 6 electrons. The d sublevel holds a maximum of 10 electrons. The f sublevel holds a maximum of 14 electrons.

The maximum electrons per level is obtained by adding the maximum number of electrons in each sublevel.


Electrons per Energy Level


Example 5.8 Energy Levels, Sublevels, & Electrons

The third energy level is split into three sublevels: 3s, 3p, and 3d. The maximum number of electrons that can occupy each sublevel is as follows:

s sublevel = 2 e–

p sublevel = 6 e–

d sublevel = 10 e–

The maximum number of electrons in the third energy level is found by adding the three sublevels together:

3s + 3p + 3d = total electrons 2 e– + 6 e– + 10 e– = 18 e–

The third energy level can hold a maximum of 18 electrons. Of course, in elements where the third energy level of an atom is not filled, there are fewer than 18 electrons.

Solution

What is the maximum number of electrons that can occupy the third energy level?

Exercise 5.8 Energy Levels, Sublevels, and Electrons

What is the maximum number of electrons that can occupy the fourth energy level?Answers: 4s, 4p, 4d, 4f; 32 e– (2 e– + 6 e– + 10 e– + 14 e–)

Practice Exercise

What is the theoretical number of sublevels in the tenth energy level?

Concept Exercise

Electron Configurations

Electrons are arranged about the nucleus in a regular manner. The first electrons fill the energy sublevel closest to the nucleus.

Electrons continue filling each sublevel until it is full, and then start filling the next closest sublevel.

A partial list of sublevels in order of increasing energy is as follows:

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d …


Filling Diagram for Energy Sublevels The order

does not strictly follow 1, 2, 3, etc.

For now, use Figure 5.16 to predict the order of sublevel filling.


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

Increasing Energy

[He][Ne] [Ar] [Kr] [Xe] [Rn]

Core

Example 5.9 Order of Sublevels

If you do not know the order of sublevels, refer to the filling diagram in Figure 5.16.

(a) Although the third energy level has 3s 3p, and 3d sublevels, the 3d sublevel does not immediately follow the 3p. Instead, the 4s sublevel follows the 3p and precedes the 3d. Thus,

3s, 3p, 4s

(b) Although the fourth energy level has 4s, 4p, 4d, and 4f sublevels, the 4f sublevel does not immediately follow the 4d. Instead, the 5p sublevel begins accepting electrons after the 4d is filled. Thus,

4p, 5s, 4d, 5p

Solution

According to increasing energy, what is the next energy sublevel after each of the following sublevels?(a) 3p (b) 4d

Figure 5.16 Filling Diagram for Energy Sublevels The order of sublevel filling is arranged according to increasing energy. Electrons first fill the 1s sublevel followed by the 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, and 6s sublevels.


Increasing Energy


Core

Exercise 5.9 Order of Sublevels

Which sublevel gains electrons after each of the following sublevels is filled?

(a) 2s (b) 5p

Practice Exercise

The energy difference between sublevels (increases/decreases) moving away from the nucleus.

Concept ExerciseFigure 5.16 Filling Diagram for Energy Sublevels The order of sublevel filling is arranged according to increasing energy. Electrons first fill the 1s sublevel followed by the 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, and 6s sublevels.


Increasing Energy


Core

Electron Configurations

The electron configuration of an atom is a shorthand method of writing the location of electrons by sublevel.

The sublevel is written followed by a superscript with the number of electrons in the sublevel. For example, if the 2p sublevel contains two electrons, it is written 2p2.

The electron sublevels are arranged according to increasing energy.


Writing Electron Configurations

First, determine how many electrons are in the atom. Bromine has 35 electrons.

Arrange the energy sublevels according to increasing energy:

1s 2s 2p 3s 3p 4s 3d … Fill each sublevel with electrons until you

have used all the electrons in the atom: Fe: 1s2 2s2 2p6 3s2 3p6 4s2 3d 10 4p5

The sum of the superscripts equals the atomic number of bromine (35).


Example 5.10 Electron Configuration

Refer to the periodic table to find the atomic number of an element.(a)The atomic number of fluorine is 9; therefore, the number of electrons is 9. We can fill sublevels with 9 electrons as follows :

F: 1s2 2s2 2p5

(b)The atomic number of strontium is 38; therefore, the number of electrons is 38. We can fill sublevels with 38 electrons as follows:

Sr: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2

To check your answer, find the total number of electrons by adding up the superscripts. The total is 38 e–; this agrees with the atomic number for Sr.

Solution

Write the predicted electron configuration for each of the following elements:(a) F (b) Sr

Exercise 5.10 Electron Configuration

Write the predicted electron configuration for each of the following elements:(a) argon (b) cadmium

Practice Exercise

Refer to the periodic table and state whether Cr or Mn has more electrons in the outermost d sublevel.

.

Concept Exercise

Quantum Mechanical Model An orbital is the region of space where there

is a high probability of finding an atom.

In the quantum mechanical atom, orbitals are arranged according to their size and shape.

The higher the energy of an orbital, the larger its size.


• All s orbitals have spherical shapes.

Shapes of p Orbitals Recall that there are three different p

sublevels.

All p orbitals have dumbbell shapes.

Each of the p orbitals has the same shape, but each is oriented along a different axis in space.


Shapes of d Orbitals Recall that there are five different d

sublevels.

Four of the d orbitals have a clover-leaf shape and one has a dumbbell and doughnut shape.


Location of Electrons in an Orbital

The orbitals are the region of space in which the electrons are most likely to be found.

An analogy for an electron in a p orbital is a fly trapped in two bottles held end to end.


Example 5.11 Atomic Orbitals

The size and energy of an orbital is indicated by the number; the shape of the orbital is designated by the letter.

(a)Size and energy are greater for a 4s orbital than for a 3s orbital, but less than for a 5s orbital. The shape of a 4s orbital—and all s orbitals—is similar to the shape of a sphere.

(b) Size and energy are greater for a 4p orbital than for a 3p orbital, but less than for a 5p orbital. The shape of a 4p orbital—and all p orbitals—is similar to the shape of a dumbbell.

Solution

Describe the relative size, energy, and shape for each of the following orbitals:(a) 4s versus 3s and 5s (b) 4p versus 3p and 5p

Exercise 5.11 Atomic Orbitals

Select the orbital in each of the following pairs that fits the description:(a) the higher energy orbital: 3p or 4p (b)(b)the larger size orbital: 4d or 5d

Practice Exercise

Which of the following statements are true according to the quantum mechanical model of the atom?

(a) Orbitals represent quantum energy levels for electrons.(b) Orbitals represent probability boundaries for electrons.(c) Orbitals can have different shapes.

Concept Exercise

Chapter Summary

Atoms are composed of protons, neutrons, and electrons.

The protons and neutrons are located in the nucleus, and the electrons are outside the nucleus.

Atoms are mostly empty space.

The number of protons is referred to as the atomic number for the atom.


Chapter Summary, Continued

All atoms of the same element have the same number of protons.

Isotopes are atoms with the same number of protons, but differing numbers of neutrons.

The mass number for an isotope is the total number of protons plus neutrons.

The atomic mass of an element is the weighted average of the masses of all the naturally occurring isotopes.


Chapter Summary, Continued

Light has properties of both waves and particles.

The particles of light are referred to as photons.

The energy of photons is quantized.

Electrons exist around the nucleus of atoms in discrete, quantized energy levels.

Electrons fill energy sublevels, starting with the lowest energy sublevel and filling each successive level of higher energy.


© 2011 Pearson Education, Inc.

Which postulate of Dalton’s atomic theory has been shown to be incorrect?

a. All atoms of an element are identical and have the same properties.

b. Atoms of different elements combine to form compounds.

c. Compounds contain atoms in small whole number ratios.

d. Atoms can combine in more than one ratio to form different compounds.


How many protons, neutrons, and electrons are in uranium-235?

a. 92 protons, 92 neutrons, 143 electronsb. 92 protons, 92 neutrons, 235 electronsc. 92 protons, 143 neutrons, 92 electronsd. 92 protons, 235 neutrons, 92 electrons


The average atomic mass of silicon is 28.09 amu. The masses of 28Si, 29Si, and 30Si are 27.977 amu, 28.976 amu, and 29.974 amu, respectively. Which is the most abundant isotope?

a. 28Sib. 29Sic. 30Sid. The isotopes are

equally abundant.


What is the maximum number of electrons that can occupy a 3d sublevel?

a. 2b. 6c. 10d. 14


What element has the electron configuration1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d2 ?

a. Cab. Gec. Prd. Zr

chapter 5 models of the atom vanessa n. prasad-permaul valencia college chm1025 chapter 5 1 © 2011...

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