Pre-IB/Pre-AP CHEMISTRY
Chapter 4 – Arrangement of Electrons in Atoms
Section 1: The Development of a New Atomic Model
Objectives:
• Be able to define: electromagnetic radiation, electromagnetic spectrum, wavelength, amplitude, frequency,
photoelectric effect, quantum (pl. quanta), photon, ground state, excited state, line emission spectrum,
continuous spectrum, energy level.
• Be able to explain the mathematical relationship between speed, wavelength, and frequency of a wave.
• Be able to describe what is meant by the wave-particle duality of light.
• Be able to discuss how the photoelectric effect and the line emission spectrum of hydrogen lead to the
development of the atomic model.
• Be able to describe the Bohr model of the atom.
A. Waves
• A wave is a method of transferring energy. This transfer does not require matter as a medium. Some waves
travel through matter (sound, water waves, etc.). Some waves do not require matter and can travel through
empty space (light).
• Waves can be described by their wavelength, amplitude, and frequency.
- A crest is the highest point on a wave.
- A trough is the lowest point on a wave.
- Wavelength is simply the length of a wave. It is the distance between two crests or two troughs.
(Measured in m, mm, or nm.)
- Amplitude is simply the height of a wave. It is the distance between the crest and trough of a wave.
Amplitude is measured in units of distance.
- Frequency is the number of waves passing a given point in a given time. It describes the energy of a
wave: the higher the frequency, the greater the energy of that wave. (Frequency is measured in hertz or
cycles per second or vibrations per second or 1/sec or sec-1 - they all mean the same thing.)
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As the wavelength increases, frequency decreases. This is called an inverse relationship.
Wavelength and amplitude give waves their distinctive properties. For example, the loudness of a sound wave is
its amplitude; the color of visible light is its wavelength.
Electromagnetic waves do not require a medium or matter in order to travel. Light is an example.
B. Properties of Light - Wave Description of Light
• Light is an electromagnetic wave.
• Visible light is a small part of the electromagnetic spectrum that humans are able to see.
• The electromagnetic spectrum consists of different kinds of light of different wavelengths.
• White light is light consisting of all colors of visible light. These colors are visible in a rainbow or through a
prism.
• The velocity of a wave is a product of its frequency and wavelength.
v= fλ
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The velocity of light through a vacuum(c) is about 3.0 x 108 m/sec. It is slightly slower through matter.
C. Photoelectric Effect
• Photoelectric effect refers to the emission of electrons from a metal when light shines on the metal.
• It was found that light of a certain frequency would cause electrons to be emitted by a particular metal. Light
below that frequency had no effect.
D. Emission Spectra
 If an object becomes hot enough it will begin to emit light.
 Max Planck suggested that hot objects emit light in specific amounts called quanta (sing. quantum). Planck
showed the relationship between a quantum of energy and the frequency of the radiation.
Equantum= hf
E. Wave-Particle Duality
• Einstein later said that light had a dual nature – it behaved as both a particle and a wave.
• Each particle of light, Einstein said, carries a particular quantum of energy. Einstein called the “particles” of light
photons, which had zero mass and carried a quantum of energy. The energy is described as:
Ephoton= hf
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Einstein explained photoelectric effect
by saying in order for an electron to be ejected
from a metal, the photon striking it must have enough energy to eject it. Different metals have stronger
attraction for their electrons than other. Therefore, some must absorb more energy than others to emit
electrons.
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The lowest energy state of an atom is called its ground state.
When a current is passed through a gas at low pressure, the atoms become “excited.” Atoms in an excited state
have a higher potential energy than their ground state. An “excited” atom will return to its ground state by
releasing energy in the form of electromagnetic radiation.
F. Hydrogen-Atom-Emission- Line Spectra
• Elements will emit radiation of certain frequencies. This reflects the energy states of its electrons and is called a
bright-line or emission spectrum. The emission spectrum of an element is like its “fingerprint”.
G. Bohr Model of Hydrogen Atom - Energy Levels
• Studying the emission spectrum of hydrogen lead Niels Bohr to the idea of energy levels. The spectrum Bohr
and others observed was the result of excited electrons releasing photons as they returned to their ground
states. The difference in the energy of photons was reflected in the different frequencies of light they observed.
Section 2: The Quantum Model of the Atom
Objectives:
• Be able to define: diffraction, interference, Heisenberg Uncertainty Principle, Quantum Theory, quantum
numbers, principal quantum number, angular momentum quantum number, magnetic quantum number, spin
quantum number.
• Be able to distinguish between the Bohr model and the quantum model of the atom.
• Be able to explain how the Heisenberg Uncertainty Principle and the Schroedinger Wave Equation led to the
idea of atomic orbitals.
• Be able to list the four quantum numbers that describe each electron in an atom.
• Be able to relate the number of sublevels corresponding to each of an atom’s main energy levels, the number of
orbitals per sublevel, and the number of orbitals per main energy level.
A. Electrons as Waves
 French scientist Louis De Broglie demonstrated that electrons had a dual nature also. De Broglie showed that
electrons behaved as waves confined to
the atom. The energy of those electrons could be found
E = hf
like that of waves:
Electron beams were shown to exhibit the wave properties of diffraction and interference.
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Werner Heisenberg tried to find the location and velocity of electrons in the atom. Heisenberg found that it is
impossible to simultaneously determine the position and velocity of an electron or any other particle (The
Heisenberg Uncertainty Principle).
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Erwin Schrödinger said that electrons had a dual nature (like light) and treated them as waves.
B. Quantum Theory
• Schrödinger’s wave equation and Heisenberg’s Uncertainty Principle laid the foundation of modern quantum
theory.
• According to the Bohr model we should be able to predict the location and velocity of an electron at any time.
• Quantum theory describes mathematically the wave properties of electrons and other very small particles.
• Quantum theory disagrees with the Bohr model and says that electrons can be found in regions of high
probability but cannot be pinpointed.
• Quantum theory describes electrons as inhabiting a three-dimensional region around the nucleus that indicates
their probable locations. These regions are called orbitals.
• Scientists use quantum numbers to describe orbitals. These numbers describe the properties of the orbitals and
the electrons that occupy them.
C. Atomic Orbitals and Quantum Numbers
 Principal Quantum Number (n) - indicates the main energy level occupied by the electron. (n) values are positive
integers only.
o As (n) increases, the electron’s energy and its average distance from the nucleus increase
o Electrons are sometimes said to be in the same electron shell.
 Angular Momentum Quantum Number (l) – indicates the shape of the orbital
o Orbitals (except for first main energy level) of different shapes (sublevels) exist for a given value of n.
Values are allowed to be zero and all positive integers less than or equal to n – 1
 s – spherical orbitals
 p – dumbbell shape
 d – more complex
o 1st energy level – only one sublevel possible (n=1, s orbital)
o 2nd energy level – two sublevels (n=2, s & p)
o 3rd energy level – three sublevels (n=3, s, p, & d)
o 4th energy level – four sublevels (n=4, s, p, d & f)
 Magnetic Quantum Number (m) – indicates the orientation of an orbital around the nucleus
o Values of m are whole numbers, including zero, from –l to +1
o s is spherical and it is centered about the nucleus, it only has only possible orientation (m=0, therefore
only one s orbital in each s sublevel)
o p orbitals extend along the x, y, or z axis of the coordinate system – there are three p orbitals in each p
sublevel (px – m = -1, py – m = 0, and pz - m = +1)
o 5 d orbitals in each d sublevel (m = -2, m = -1, m = 0, m = +1, m = +2)
o 7 f orbitals in each f sublevel