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Atoms: The Building Blocks of Matter. Foundations of Atomic Theory. Nearly all chemists in late 1700s accepted the definition of an element as a substance that cannot be broken down further Knew about chemical reactions

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Atoms the building blocks of matter

Atoms: The Building Blocks of Matter


Foundations of atomic theory

Foundations of Atomic Theory

  • Nearly all chemists in late 1700s accepted the definition of an element as a substance that cannot be broken down further

  • Knew about chemical reactions

  • Great disagreement as to whether elements always combine in the same ratio when forming a specific compound


Law of conservation of mass

Law of Conservation of Mass

  • With the help of improved balances, investigators could accurately measure the masses of the elements and compounds they were studying

  • This lead to discovery of several basic laws

  • Law of conservation of mass states that mass is neither destroyed nor created during ordinary chemical reactions or physical changes


Law of definite proportions

Law of Definite Proportions

  • law of definite proportions  A chemical compound contains the same elements in exactly the same proportions by mass regardless of the size of the sample or source of the compound

Each of the salt crystals shown here contains exactly

39.34% sodium and 60.66% chlorine by mass.


Law of multiple proportions

Law of Multiple Proportions

  • Two elements sometimes combine to form more than one compound

    • For example, the elements carbon and oxygen form two compounds, carbon dioxide and carbon monoxide

  • Consider samples of each of these compounds, each containing 1.0 g of carbon


Atoms the building blocks of matter

  • In carbon dioxide, 2.66 g of oxygen combine with 1.0 g of carbon

  • In carbon monoxide, 1.33 g of oxygen combine with 1.0 g of carbon


Atoms the building blocks of matter

  • The ratio of the masses of oxygen in these two compounds is exactly 2.66 to 1.33, or 2 to 1


1808 john dalton

1808 John Dalton

  • Proposed an explanation for the law of conservation of mass, the law of definite proportions, and the law of multiple proportions


Atoms the building blocks of matter

  • He reasoned that elements were composed of atoms and that only whole numbers of atoms can combine to form compounds


Atoms the building blocks of matter

  • His theory can be summed up by the following statements


Dalton s atomic theory

Dalton’s Atomic Theory

  • All matter is composed of extremely small particles called atoms.

  • Atoms of a given element are identical in size, mass, and other properties; atoms of different elements differ in size, mass, and other properties.

  • Atoms cannot be divided, created or destroyed.

  • Atoms of different elements combine in simple whole-number ratios to form chemical compounds.

  • In chemical reactions, atoms are combined, separated, or rearranged.


Modern atomic theory

Modern Atomic Theory

  • Dalton turned Democritus’sidea into a scientific theory which was testable

  • Not all parts of his theory have been proven correct


Atoms the building blocks of matter

  • Ex. We know atoms are divisible into even smaller particles

  • We know an element can have atoms with different masses


Structure of the atom

Structure of the Atom


All atoms consist of two regions

All atoms consist of two regions

  • Nucleus very small region located near the center of an atom

    • In the nucleus there is at least one positively charged particle called the proton

    • Usually at least one neutral particle called the neutron

  • Surrounding the nucleus is a region occupied by negatively charged particles called electrons


Discovery of the electron

Discovery of the Electron

  • Resulted from investigations into the relationship between electricity and matter

  • Late 1800s, many experiments were performed  electric current was passed through different gases at low pressures


Atoms the building blocks of matter

  • These experiments were carried out in glass tubes known as cathode-ray tubes


Cathode rays and electrons

Cathode Rays and Electrons

  • Investigators noticed that when current was passed through a cathode-ray tube, the opposite end of the tube glowed


Atoms the building blocks of matter

  • Hypothesized that the glow was caused by a stream of particles, which they called a cathode ray

  • The ray traveled from the cathode to the anode when current was passed through the tube


Observations

Observations

  • 1. cathode rays deflected by magnetic field in same way as wire carrying electric current (known to have negative charge)

  • 2. rays deflected away from negatively charged object


Atoms the building blocks of matter

  • Observations led to the hypothesis that the particles that compose cathode rays are negatively charged

  • Strongly supported by a series of experiments carried out in 1897 by the English physicist Joseph John Thomson


Atoms the building blocks of matter

  • He was able to measure the ratio of the charge of cathode-ray particles to their mass

  • He found that this ratio was always the same, regardless of the metal used to make the cathode or the nature of the gas inside the cathode-ray tube


Atoms the building blocks of matter

  • Thomson concluded that all cathode rays are composed of identical negatively charged particles, which were later named electrons


Charge and mass of the electron

Charge and Mass of the Electron

  • Confirmed that the electron carries a negative electric charge

  • Because cathode rays have identical properties regardless of the element used to produce them, it was concluded that electrons are present in atoms of all elements


Atoms the building blocks of matter

  • Cathode-ray experiments provided evidence that atoms are divisible and that one of the atom’s basic constituents is the negatively charged electron


Atoms the building blocks of matter

  • Thomson’s experiment revealed that the electron has a very large charge for its tiny mass

  • Mass of the electron is about one two-thousandth the mass of the simplest type of hydrogen atom (the smallest atom known)

  • Since then found that the electron has a mass of 9.109 × 10−31 kg, or 1/1837 the mass of the hydrogen atom


Atoms the building blocks of matter

  • Based on information about electrons, two inferences made about atomic structure

  • b/c atoms are neutral they must have positive charge to balance negative electrons

  • b/c electrons have very little mass, atoms must have some other particles that make up most of the mass


Thomson s atom

Thomson’s Atom

  • Plum pudding model (based on English dessert)

  • Negative electrons spread evenly through positive charge of the rest of the atom

  • Like seeds in a watermelon


Discovery of atomic nucleus

Discovery of Atomic Nucleus

  • 1911 by New Zealander Ernest Rutherford and his associates Hans Geiger and Ernest Marsden

  • Bombarded a thin, gold foil with fast-moving alpha particles (positively charged particles with about four times the mass of a hydrogen atom)


Atoms the building blocks of matter

  • Assume mass and charge were uniformly distributed throughout atoms of gold foil (from Thomson’s model of the atom)

  • Expected alpha particles to pass through with only slight deflection


What really happened

What Really Happened…

  • Most particles passed with only slight deflection

  • However, 1/8,000 were found to have a wide deflection


Atoms the building blocks of matter

  • Rutherford explained later it was “as if you have fired a 15-inch artillery shell at a piece of tissue paper and it came back and hit you.”


Explanation

Explanation

  • After 2 years, Rutherford finally came up with an explanation

  • The rebounded alpha particles must have experienced some powerful force within the atom


Atoms the building blocks of matter

  • The source of this force must occupy a very small amount of space because so few of the total number of alpha particles had been affected by it


Atoms the building blocks of matter

  • The force must be caused by a very densely packed bundle of matter with a positive electric charge

  • Rutherford called this positive bundle of matter the nucleus


Atoms the building blocks of matter

  • Rutherford had discovered that the volume of a nucleus was very small compared with the total volume of an atom

  • If the nucleus were the size of a marble, then the size of the atom would be about the size of a football field

  • But where were the electrons?


Atoms the building blocks of matter

  • Rutherford suggested that the electrons surrounded the positively charged nucleus like planets around the sun

  • He could not explain, however, what kept the electrons in motion around the nucleus


Rutherford s atom

Rutherford’s Atom


Composition of atomic nucleus

Composition of Atomic Nucleus

  • Except hydrogen, all atomic nuclei made of two kinds of particles

    • Protons

    • Neutrons


Atoms the building blocks of matter

  • Protons = positive

  • Neutrons = neutral

  • Electrons = negative


Atoms the building blocks of matter

  • Atoms are electrically neutral, so number of protons and electrons IS ALWAYS THE SAME


Atoms the building blocks of matter

  • The nuclei of atoms of different elements differ in the number of protons they contain and therefore in the amount of positive charge they possess

  • So the number of protons in an atom’s nucleus determines that atom’s identity


Forces in the nucleus

Forces in the Nucleus

  • Usually, particles that have the same electric charge repel one another

  • Would expect a nucleus with more than one proton to be unstable


Atoms the building blocks of matter

  • When two protons are extremely close to each other, there is a strong attraction between them


Atoms the building blocks of matter

  • Nuclear forces short-range proton-neutron, proton-proton, and neutron-neutron forces that hold the nuclear particles together


The sizes of atoms

The Sizes of atoms

  • Area occupied by electrons is electron cloud – cloud of negative charge

  • Radius of atom is distance from center of nucleus to outer portion of cloud


Atoms the building blocks of matter

  • Unit – picometer (10-12 m)

  • Atomic radii range from 40-270 pm

  • Very high densities – 2 x 108 tons/cm3


Counting atoms

Counting Atoms


Atomic number

Atomic Number

  • Atoms of different elements have different numbers of protons

  • Atomic number (Z) number of protons in the nucleus of each atom of that element

  • Shown on periodic table

  • Atomic number identifies an element

3

Li

Lithium

6.941

[He]2s1


Isotopes

Isotopes

  • Hydrogen and other atoms can contain different numbers of neutrons


Atoms the building blocks of matter

  • Isotope atoms of same element that have different masses


Isotopes of hydrogen

Isotopes of Hydrogen


Mass number

Mass Number

  • Mass number total number of protons and neutrons in the nucleus of an isotope


Sample problem

Sample Problem

  • How many protons, electrons, and neutrons are there in an atom of chlorine-37?


Atoms the building blocks of matter

  • atomic number = number of protons = number of electrons

  • mass number = number of neutrons + number of protons


Atoms the building blocks of matter

  • mass number of chlorine-37 − atomic number of chlorine = number of neutrons in chlorine-37

  • mass number − atomic number = 37 (protons plus neutrons) − 17 protons = 20 neutrons


Practice problems

Practice Problems

  • How many protons, electrons, and neutrons are in an atom of bromine-80?

  • Answer 35 protons, 35 electrons, 45 neutrons


Atoms the building blocks of matter

2. Write the nuclear symbol for carbon-13.

  • Answer 136C


Atoms the building blocks of matter

3. Write the hyphen notation for the element that contains 15 electrons and 15 neutrons.

  • Answer phosphorus-30


Relative atomic masses

Relative Atomic Masses

  • Because atoms are so small, scientists use a standard to control the units of atomic mass  carbon-12

  • Randomly assigned a mass of exactly 12 atomic mass units (amu)


Atoms the building blocks of matter

  • 1 amu is exactly 1/12 the mass of a carbon-12 atom

  • Atomic mass of any atom determined by comparing it with mass of C-12

  • Ex. H  1/12 C-12, so 1 amu


Average atomic masses

Average Atomic Masses

  • Average atomic mass the weighted average of the atomic masses of the naturally occurring isotopes of an element


Atoms the building blocks of matter

  • Ex. You have a box containing 2 size of marbles

    • 25% are 2.00g each

    • 75% are 3.00g each

      25% = 0.2575% = 0.75

      (2.00g x 0.25) + (3.00g x 0.75) = 2.75g


Calculating average atomic mass

Calculating Average Atomic Mass

Copper

69.17% Cu-63 – 62.929599 amu

30.83% Cu-65 – 64.927793 amu

(0.6917 x 62.929599) + (0.3083 x 64.927793)

= 63.55 amu


Relating mass to numbers of atoms

Relating Mass to Numbers of Atoms

  • The relative atomic mass scale makes it possible to know how many atoms of an element are present in a sample of the element with a measurable mass


Atoms the building blocks of matter

  • Three very important concepts provide the basis for relating masses in grams to numbers of atoms

  • The mole

  • Avogadro’s number

  • Molar mass


The mole

The Mole

  • SI unit for an amount of substance (like 1 dozen = 12)

  • Mole (mol)  amount of a substance that contains as many particles as there are atoms in exactly 12g of C-12


Avogadro s number

Avogadro’s Number

  • Avogadro’s number the number of particles in exactly one mole of a pure substance

  • 6.022 x 1023

  • How big is that?


Atoms the building blocks of matter

  • If 5 billion people worked to count the atoms in one mole of an element, and if each person counted continuously at a rate of one atom per second, it would take about 4 million years for all the atoms to be counted


Molar mass

Molar Mass

  • Molar mass the mass of one mole of a pure substance

  • Written in unit g/mol


Atoms the building blocks of matter

  • Found on periodic table (atomic mass)

  • Ex. Molar mass of H = 1.008 g/mol


Example

Example

How many grams of helium are there in 2 moles of helium?

2.00 mol He x = ? g He

2.00 mol He x 4.00 g He= 8.00 g He

1 mole He


Practice problems1

Practice Problems

What is the mass in grams of 3.50 mol of the element copper, Cu?

222 g Cu

What is the mass in grams of 2.25 mol of the element iron, Fe?

126 g Fe


Atoms the building blocks of matter

What is the mass in grams of 0.375 mol of the element potassium, K?

14.7 g K

What is the mass in grams of 0.0135 mol of the element sodium, Na?

0.310 g Na


Atoms the building blocks of matter

What is the mass in grams of 16.3 mol of the element nickel, Ni?

957 g Ni


Atoms the building blocks of matter

A chemist produced 11.9 g of aluminum, Al. How many moles of aluminum were produced?

0.441 mol Al


Atoms the building blocks of matter

How many moles of calcium, Ca, are in 5.00 g of calcium?

0.125 mol Ca


Atoms the building blocks of matter

How many moles of gold,Au, are in 3.60 × 10−10 g of gold?

1.83 × 10−12 mol Au


Conversions with avogadro s number

Conversions with Avogadro’s Number

How many moles of silver, Ag, are in 3.01 x 1023 atoms of silver?

Given: 3.01 × 1023 atoms of Ag

Unknown: amount of Ag in moles

Ag atoms ×= moles Ag

3.01x1023atomsAg x =0.500 mol Ag


Practice problems2

Practice problems

How many moles of lead, Pb, are in 1.50 × 1012 atoms of lead?

2.49 × 10−12 mol Pb


Atoms the building blocks of matter

How many moles of tin, Sn, are in 2500 atoms of tin?

4.2 × 10−21 mol Sn


Atoms the building blocks of matter

How many atoms of aluminum, Al, are in 2.75 mol of aluminum?

1.66 × 1024 atoms Al


Atoms the building blocks of matter

What is the mass in grams of 7.5 × 1015 atoms of nickel, Ni?

7.3 × 10−7 g Ni


Atoms the building blocks of matter

How many atoms of sulfur, S, are in 4.00 g of sulfur?

7.51 × 1022 atoms S


Atoms the building blocks of matter

What mass of gold,Au, contains the same number of atoms as 9.0 g of aluminum,Al?

66 g Au


Arrangement of electrons in atoms

Arrangement of Electrons in Atoms


Atoms the building blocks of matter

  • Visible light is a kind of electromagnetic radiation form of energy that exhibits wavelike behavior as it travels through space

    • X-rays, UV, infrared, etc.

  • Together, all forms of electromagnetic radiation form the electromagnetic spectrum


Properties of em radiation

Properties of EM Radiation

  • All forms of EM radiation travel at a constant speed (3.0 × 108 m/s) through a vacuum and at slightly slower speeds through matter


Atoms the building blocks of matter

  • It has a repetitive nature, which can be described by the measurable properties  wavelength and frequency


Atoms the building blocks of matter

  • Wavelength (λ)  the distance between corresponding points on neighboring waves

  • Frequency (ν)  the number of waves that pass a given point in a specific time, usually one second


The photoelectric effect

The Photoelectric Effect

  • Early 1900s, scientists conducted two experiments involving relations of light and matter that could not be explained by the wave theory of light


Atoms the building blocks of matter

  • One experiment involved a phenomenon known as the photoelectric effect

  • Photoelectric effect  the emission of electrons from a metal when light shines on the metal


The mystery

The Mystery

  • For a given metal, no electrons were emitted if the light’s frequency was below a certain minimum—regardless of how long the light was shone

  • Light was known to be a form of energy, capable of knocking loose an electron from a metal


Atoms the building blocks of matter

  • Wave theory of light predicted light of any frequency could supply enough energy to eject an electron

  • Couldn’t explain why light had to be a minimum frequency in order for the photoelectric effect to occur


The particle description of light

The Particle Description of Light

  • Explanation  1900, German physicist Max Planck was studying the emission of light by hot objects

  • Proposed a hot object does not emit electromagnetic energy continuously, as would be expected if the energy emitted were in the form of waves


Atoms the building blocks of matter

  • Instead, Planck suggested the object emits energy in small, specific amounts called quanta

  • Quantum  the minimum quantity of energy that can be lost or gained by an atom


Atoms the building blocks of matter

  • Planck projected the following relationship between a quantum of energy and the frequency of radiation

    E = hν

  • In the equation,

    • E is the energy, in joules, of a quantum of radiation

    • ν is the frequency of the radiation emitted

    • h is a constant now known as Planck’s constant

      • h = 6.626 × 10−34 J• s


1905 albert einstein

1905 Albert Einstein

  • Expanded on Planck’s theory by introducing the idea that electromagnetic radiation has a dual wave-particle nature

  • Light displays many wavelike properties, it can also be thought of as a stream of particles


Atoms the building blocks of matter

  • Einstein called these particles photons

  • Photon aparticle of electromagnetic radiation having zero mass and carrying a quantum of energy


Atoms the building blocks of matter

  • The energy of a specific photon depends on the frequency of the radiation

    Ephoton = hν


The hydrogen atom line emission spectrum

The Hydrogen-Atom Line-Emission Spectrum

  • When current is passed through a gas at low pressure, the potential energy of some of the gas atoms increases


Atoms the building blocks of matter

  • The lowest energy state of an atom is its ground state

  • A state in which an atom has a higher potential energy than it has in its ground state is an excited state


Returning to ground state

Returning to Ground State

  • When an excited atom returns to its ground state, it gives off the energy it gained in the form of electromagnetic radiation

  • Example of this process is a neon sign

Excited neon atoms emit light when falling back to the ground state or to a lower-energy excited state.


Atoms the building blocks of matter

  • Whenever an excited hydrogen atom falls back from an excited state to its ground state or to a lower-energy excited state, it emits a photon of radiation

  • The energy of this photon (Ephoton = hν) is equal to the difference in energy between the atom’s initial state and its final state


Atoms the building blocks of matter

  • Changes of energy (transition of an electron from one orbit to another) is done in isolated quanta

  • Quanta are not divisible

  • There is sudden movement from one specific energy level to another, with no smooth transition

  • There is no ``in-between‘‘


Atoms the building blocks of matter

  • Hydrogen atoms emit only specific frequencies of light  showed that energy differences between the atoms’ energy states were fixed

  • The electron of a hydrogen atom exists only in very specific energy states


Bohr model of the hydrogen atom

Bohr Model of the Hydrogen Atom

  • Solved in 1913 by the Danish physicist Niels Bohr

  • Proposed a model of the hydrogen atom that linked the atom’s electron with photon emission


Atoms the building blocks of matter

  • According to the model, the electron can circle the nucleus only in allowed paths, or orbits


Atoms the building blocks of matter

  • When the electron is in one of these orbits, the atom has a definite, fixed energy

  • The electron, and therefore the hydrogen atom, is in its lowest energy state when it is in the orbit closest to the nucleus


Atoms the building blocks of matter

  • This orbit is separated from the nucleus by a large empty space where the electron cannot exist

  • The energy of the electron is higher when it is in orbits farther from the nucleus


The rungs of a ladder

The Rungs of a Ladder

  • The electron orbits or atomic energy levels in Bohr’s model can be compared to the rungs of a ladder

  • When you are standing on a ladder, your feet are on one rung or another


Atoms the building blocks of matter

  • The amount of potential energy that you possess relates to standing on the first rung, the second rung…

  • Your energy cannot relate to standing between two rungs because you cannot stand in midair


Atoms the building blocks of matter

  • In the same way, an electron can be in one orbit or another, but not in between


Moving up in the orbit

Moving up in the Orbit…

  • Explaining spectral lines:

  • While in a given orbit, electron isn’t gaining or losing energy


Atoms the building blocks of matter

  • Can move to higher-energy orbit by gaining energy equal to difference in energy between higher-energy orbit and initial lower-energy orbit


Atoms the building blocks of matter

  • When hydrogen is excited, electron is in higher-energy orbit

  • When electron falls to lower energy level, a photon is emitted in process called emission


Atoms the building blocks of matter

  • Photon’s energy is equal to energy difference between initial high energy and final lower energy level

  • To move electron from low energy to high energy level, energy must be added to atom in process called absorption


Atoms the building blocks of matter

  • When a hydrogen atom is in an excited state, its electron is in a higher-energy orbit

  • When the atom falls back from the excited state, the electron drops down to a lower-energy orbit


Atoms the building blocks of matter

  • In the process, a photon is emitted that has an energy equal to the energy difference between the initial higher-energy orbit and the final lower-energy orbit


Electrons as waves

Electrons as Waves

  • Photoelectric effect and H spectrum showed light behaving as wave and particle


Atoms the building blocks of matter

  • Could electrons have dual wave-particle nature?

  • 1924 Louis de Broglie proposed answer that revolutionized our understanding of matter


Atoms the building blocks of matter

  • DeBroglie pointed out behavior of electrons in Bohr’s orbits similar to known behavior of waves


Atoms the building blocks of matter

  • Any wave in limited space has only certain frequencies

  • Electrons should be considered as being in limited space around the nucleus


Atoms the building blocks of matter

  • So electron waves could exist only at specific frequencies

  • According to E = hv, frequencies will correspond to specific energies – the quantized energies of Bohr’s orbits


The heisenberg uncertainty principle

The Heisenberg Uncertainty Principle

  • If electrons are both particles and waves, then where are they in the atom?

  • To answer this question, it is important to consider a proposal first made in 1927 by the German theoretical physicist Werner Heisenberg


Atoms the building blocks of matter

  • Heisenberg’s idea involved detection of electrons by interaction with photons

  • Photons have about same energy as electrons

  • Trying to locate specific electron with photon knocks electron off course


Atoms the building blocks of matter

  • So there is always uncertainty trying to locate an electron

  • Heisenberg uncertainty principlestates that it is impossible to determine simultaneously both the position and velocity of an electron or any other particle


Schrodinger wave equation

Schrodinger Wave Equation

  • Used hypothesis that electrons have dual nature to develop equation that treated electrons in atoms as waves

  • Bohr assumed quantization was fact

  • Schrodinger didn’t assume – it was a natural result of his equation


Atoms the building blocks of matter

  • Only waves of specific energies (frequencies) provided solutions to equation

  • With Heisenberg uncertainty, wave equation laid foundation for modern quantum theory


Atoms the building blocks of matter

  • Quantum theory – describes mathematically the wave properties of electrons and other small particles


Orbitals

Orbitals

  • Electrons do not travel around the nucleus in neat orbits

  • Instead, they exist in certain regions called orbitals


Atoms the building blocks of matter

  • Orbital  a three-dimensional region around the nucleus that indicates the probable location of an electron


Atomic orbitals and quantum numbers

Atomic Orbitals and Quantum Numbers

  • Bohr’s model – electrons of increasing energy occupy orbits farther and farther from nucleus


Atoms the building blocks of matter

  • Schrodinger equation – electrons in orbitals have quantized energies

  • Energy level is not the only characteristic of an orbital shown by solving Schrodinger equation


Atomic orbitals and quantum numbers1

Atomic Orbitals and Quantum Numbers

  • In order to completely describe orbitals, scientists use quantum numbers

  • Quantum numbers  specify the properties of atomic orbitals and theproperties of electrons in orbitals


Atoms the building blocks of matter

  • First 3 numbers result from solutions to Schrodinger’s equation

  • Indicate energy level, shape, and orientation of each orbital


The quantum numbers

The Quantum Numbers

  • Principal quantum number  the main energy level occupied by the electron

  • Angular momentum quantum number  the shape of the orbital

  • Magnetic quantum number  the orientation of the orbital around the nucleus

  • Spin quantum number  the two fundamental spin states of an electron in an orbital


Principal quantum number

Principal Quantum Number

  • Symbolized by n

  • Indicates the main energy level occupied by the electron

  • Values are positive integers only

  • As n increases, the electron’s energy and its average distance from the nucleus increase


Angular momentum quantum number

Angular Momentum Quantum Number

  • Except at the first main energy level, orbitals of different shapes— known as sublevels—exist for a given value of n

  • The angular momentum quantum number, symbolized by l, indicates the shape of the orbital


Atoms the building blocks of matter

  • The values of l allowed are zero and all positive integers less than or equal to n − 1

    • n = 2 can have one of two shapes

    • l = 0 and l = 1


Atoms the building blocks of matter

n = 1

  • l = 0 only

  • For l = 0, the corresponding letter designation for the orbital shape is s

  • Shape of s is a sphere


Atoms the building blocks of matter

n = 2

  • l = 0 (s), l = 1 (p)

  • For l = 1, , the corresponding letter designation for the orbital shape is p

  • Shape of p is


Atoms the building blocks of matter

n = 3

  • l = 0 (s), l = 1 (p), l = 2 (d)

  • For l = 2, the corresponding letter designation for the orbital shape is d

  • Shape of d is


Atoms the building blocks of matter

n= 4

  • l = 0 (s),1 (p), 2 (d), 3 (f)

  • For l = 3, the corresponding letter designation for the orbital shape is f

  • Shape is too complicated to picture


Atoms the building blocks of matter

  • Each atomic orbital is designated by the principal quantum number followed by the letter of the sublevel

  • For example, the 1s sublevel is the s orbital in the first main energy level, while the 2p sublevel is the set of p orbitals in the second main energy level


Magnetic quantum number

Magnetic Quantum Number

  • Atomic orbitals can have the same shape but different orientations around the nucleus

  • The magnetic quantum number, symbolized by m, indicates the orientation of an orbital around the nucleus


S orbital

S orbital

  • Because an s orbital is spherical and is centered around the nucleus, it has only one possible orientation

  • This orientation corresponds to a magnetic quantum number of m = 0

  • There is therefore only one s orbital in each s sublevel


P orbital

P orbital

  • p orbital can extend along the x, y, or z axis

  • There are therefore three porbitals in each p sublevel, which are designated as px, py, and pzorbitals

  • The three porbitals occupy different regions of space and correspond, in no particular order, to values of m = −1, m = 0, and m = +1


D orbital

D orbital

  • There are five different d orbitals in each d sublevel

  • The five different orientations, including one with a different shape, correspond to values of m = −2, m = −1, m = 0, m = +1, and m = +2


Spin quantum number

Spin Quantum Number

  • An electron in an orbital can be thought of as spinning on an axis

  • It spins in one of two possible directions, or states

  • The spin quantum number has only two possible values — +1/2 , −1/2


Atoms the building blocks of matter

  • Indicate the two fundamental spin states of an electron in an orbital

  • ***A single orbital can hold a maximum of two electrons, which must have opposite spins***


Electron configurations

Electron Configurations


Atoms the building blocks of matter

  • Quantum model of atom better than Bohr model b/c it describes the arrangements of electrons in atoms other than hydrogen

  • Electron configuration the arrangement of electrons in an atom

  • b/c atoms of different elements have different numbers of e-, the e- configuration for each element is unique


Atoms the building blocks of matter

  • Electrons in atoms assume arrangements that have lowest possible energies

  • Ground-state electron configuration lowest-energy arrangement of electrons for each element

  • Some rules combined with quantum numbers let us determine the ground-state e- configurations


Rules governing electron configurations

Rules Governing Electron Configurations

  • To build up electron configurations for the ground state of any particular atom, first the energy levels of the orbitals are determined


Atoms the building blocks of matter

  • Then electrons are added to the orbitals one by one according to three basic rules

  • Aufbau principle

  • Pauli exclusion principle

  • Hund’s rule


Aufbau principle

Aufbau Principle

  • The first rule shows the order in which electrons occupy orbitals

  • According to the Aufbau principle, an electron occupies the lowest-energy orbital that can receive it


Atoms the building blocks of matter

  • The orbital with the lowest energy is the 1s orbital

  • Ground-state hydrogen atom  electron in this orbital


Atoms the building blocks of matter

  • The 2s orbital is the next highest in energy, then the 2p orbitals

  • Beginning with the third main energy level, n = 3, the energies of the sublevels in different main energy levels begin to overlap


Atoms the building blocks of matter

  • The 4s sublevel is lower in energy than the 3d sublevel

  • Therefore, the 4s orbital is filled before any electrons enter the 3d orbitals

  • (Less energy is required for two electrons to pair up in the 4s orbital than for a single electron to occupy a 3d orbital)


Pauli exclusion principle

Pauli Exclusion Principle

  • The second rule reflects the importance of the spin quantum number

  • According to the Pauli exclusion principle, no two electrons in the same atom can have the same set of four quantum numbers


Hund s rule

Hund’s Rule

  • The third rule requires placing as many unpaired electrons as possible in separate orbitals in the same sublevel

  • Electron-electron repulsion is minimized  the electron arrangements have the lowest energy possible


Atoms the building blocks of matter

  • Hund’s rule orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron, and all electrons in singly occupied orbitals must have the same spin


Orbital notation

Orbital Notation


Electron configuration notation

Electron-Configuration Notation

  • Electron-configuration notation eliminates the lines and arrows of orbital notation

  • Instead, the number of electrons in a sublevel is shown by adding a superscript to the sublevel designation


Atoms the building blocks of matter

  • The hydrogen configuration is represented by 1s1

  • The superscript indicates that one electron is present in hydrogen’s 1s orbital


Atoms the building blocks of matter

  • The helium configuration is represented by 1s2

  • Here the superscript indicates that there are two electrons in helium’s 1s orbital


Sample problem1

Sample Problem

The electron configuration of boron is 1s22s22p1. How many electrons are present in an atom of boron? What is the atomic number for boron? Write the orbital notation for boron.


Practice problems3

Practice Problems

  • The electron configuration of nitrogen is 1s22s22p3. How many electrons are present in a nitrogen atom? What is the atomic number of nitrogen? Write the orbital notation for nitrogen.


Practice problems4

Practice Problems

The electron configuration of fluorine is 1s22s22p5. What is the atomic number of fluorine? How many of its p orbitals are filled? How many unpaired electrons does a fluorine atom contain?

  • Answer

  • 9

  • 2

  • 1


Elements of the second period

Elements of the Second Period

  • According to Aufbau principle, after 1s orbital is filled, the next electron occupies the s sublevel in the second main energy level

  • Lithium, Li, has a configuration of 1s22s1

  • The electron occupying the 2s level of a lithium atom is in the atom’s highest, or outermost, occupied level


Atoms the building blocks of matter

  • The highest occupied level  the electron-containing main energy level with the highest principal quantum number

  • The two electrons in the 1s sublevel of lithium are no longer in the outermost main energy level

  • They have become inner-shell electronselectrons that are not in the highest occupied energy level


Atoms the building blocks of matter

  • The fourth electron in an atom of beryllium, Be, must complete the pair in the 2s sublevel because this sublevel is of lower energy than the 2p sublevel

  • With the 2s sublevel filled, the 2p sublevel, which has three vacant orbitals of equal energy, can be occupied


Atoms the building blocks of matter

  • One of the three p orbitals is occupied by a single electron in an atom of boron, B

  • Two of the three p orbitals are occupied by unpaired electrons in an atom of carbon, C

  • And all three p orbitals are occupied by unpaired electrons in an atom of nitrogen, N


Elements of third period

Elements of Third Period

  • After the outer octet is filled in neon, the next electron enters the s sublevel in the n = 3 main energy level


Atoms the building blocks of matter

  • Atoms of sodium, Na, have the configuration 1s22s22p63s1

  • Once past Neon, can use Noble-gas notation


Noble gas notation

Noble-Gas Notation

  • The Group 18 elements (helium, neon, argon, krypton, xenon, and radon) are called the noble gases


Atoms the building blocks of matter

  • To simplify sodium’s notation, the symbol for neon, enclosed in square brackets, is used to represent the complete neon configuration:

    [Ne] = 1s22s22p6

  • This allows us to write sodium’s electron configuration as [Ne]3s1, which is called sodium’s noble-gas notation


Elements of the fourth period

Elements of the Fourth Period

  • Period begins by filling 4s orbital (empty orbital of lowest energy)

  • First element in fourth period is potassium, K

  • E- configuration [Ar]4s1

  • Next element is calcium, Ca

  • E- configuration [Ar]4s2


Atoms the building blocks of matter

  • With 4s sublevel filled, 4p and 3d sublevels are next available empty orbitals

  • Diagram shows 3d sublevel is lower energy than 4p sublevel

  • So 3d is filled next


Atoms the building blocks of matter

  • Total of 10 electrons can fill 3d orbitals

  • These are filled from element scandium (Sc) to zinc (Zn)


Atoms the building blocks of matter

  • Scandium has e- configuration [Ar]3d14s2

  • Titanium, Ti, has configuration [Ar]3d24s2

  • Vanadium, V, has configuration [Ar]3d34s2

  • Up to this point, 3 e- with same spin added to 3 separate d orbitals (required by Hund’s rule)


Atoms the building blocks of matter

  • Chromium, Cr, has configuration [Ar]3d54s1

  • We added one electron to 4th 3d orbital

  • We also took a 4s electron and added it to 5th 3d orbital

  • Seems to be against Aufbau principle

  • In reality, [Ar]3d54s1 is lower energy than [Ar]3d44s2


Atoms the building blocks of matter

  • Having 6 outer orbitals with unpaired electrons in 3d orbital is more stable than having 4 unpaired electrons in 3d orbitals and forcing 2 electrons to pair in 4s

  • For tungsten, W, (same group as chromium) having 4 e- in 5d orbitals and 2 e- paired in 6s is most stable arrangement

  • No easy explanantion


Atoms the building blocks of matter

  • Manganese, Mn, has configuration [Ar]3d54s2

  • Added e- goes to 4s orbital, completely filling it and leaving 3d half-filled

  • Starting with next element, e- continue to pair in d orbitals


Atoms the building blocks of matter

  • So iron, Fe, has configuration [Ar]3d64s2

  • Cobalt, Co, has [Ar]3d74s2

  • Nickel, Ni, has [Ar]3d84s2


Atoms the building blocks of matter

  • With copper, Cu, an electron from 4s moves to pair with e- in 5th 3d orbital

  • Configuration: [Ar]3d104s1 (most stable)

  • For zinc, Zn, 4s sublevel filled to give [Ar]3d104s2

  • For next elements, 1 e- added to 4p orbitals according to Hund’s rule


Elements of fifth period

Elements of Fifth Period

  • In 18 elements of 5th period, sublevels fill in similar way to 4th period elements

  • BUT they start at 5s level instead of 4s level

  • Fill 5s, then 4d, and finally 5p

  • There are exceptions just like in 4th period


Practice problem

Practice Problem

Write both the complete electron-configuration notation and the noble-gas notation for iron, Fe.


Atoms the building blocks of matter

Write both the complete electron configuration notation and the noble-gas notation for iodine, I. How many inner-shell electrons does an iodine atom contain?

  • 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p65s2 4d10 5p5

  • [Kr]4d10 5s2 5p5

  • 46


Atoms the building blocks of matter

How many electron-containing orbitals are in an atom of iodine? How many of these orbitals are filled? How many unpaired electrons are there in an atom of iodine?

  • 27

  • 26

  • 1


Atoms the building blocks of matter

Write the noble-gas notation for tin, Sn. How many unpaired electrons are there in an atom of tin?

  • [Kr] 5s2 4d10 5p2

  • 2


Atoms the building blocks of matter

Without consulting the periodic table or a table in this chapter, write the complete electron configuration for the element with atomic number 25.

  • 1s2 2s2 2p6 3s2 3p6 4s2 3d5


Elements of 6 th and 7 th periods

Elements of 6th and 7th periods

  • 6th period has 32 elements

  • To build up e- configurations for elements in this period, e- first added first to 6s orbital in cesium, Cs, and barium, Ba


Atoms the building blocks of matter

  • Then in lanthanum, La, e- added to 5d orbital


Atoms the building blocks of matter

  • With next element, cerium, Ce, 4f orbitals begin to fill

  • Ce: [Xe]4f15d16s2

  • In next 13 elements, 4f orbitals filled


Atoms the building blocks of matter

  • Next 5d orbitals filled

  • Period finished by filling 6p orbitals

  • (some exceptions happen)


Practice problem1

Practice Problem

Write both the complete electron-configuration notation and the noble-gas notation for a rubidium atom.

  • 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s1

  • [Kr]5s1


Atoms the building blocks of matter

Write both the complete electron configuration notation and the noble-gas notation for a barium atom.

  • 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2

  • [Xe]6s2


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