Arrangement of Electrons in Atoms

CHAPTER 4

The Development of a New

Atomic Model

• The Rutherford model was a great improvement over the Thomson model of the atom.

• But, there was one major question that needed to be answered.

• If the electrons are negatively charged and the nucleus is positively charged, what prevents the electrons from being drawn into the nucleus of an atom?

Properties of Light

• Prior to 1900, most scientists believed that light behaved as waves.

• Later, we found that light actually behaves as light and as particles.

• Most of light’s behavior is due to its wave-like behavior.

Electromagnetic Radiation

• Electromagnetic radiation is any form of energy that exhibits wavelike behavior as it travels through space.

• Examples include X-rays, UV light, microwaves, visible light, and radio waves.

• All forms of EMR travel at the same speed, 3.0 x 108 m/s. This is called the speed of light.

Electromagnetic Spectrum Light as Waves• Light is repetitive in nature like waves.

• Most of the measurable properties of waves are wavelength and frequency.

• Wavelength (!) is the distance between corresponding points on adjacent waves.

• Wavelength is measured mostly in nanometers (nm).

• (1nm = 1 x 10-9 m)

Light as Waves

(continued)

• Frequency (") is defined as the number of waves that pass a given point in a specific time, usually one second.

• Frequency is measured in hertz (Hz).

• 1 hertz = 1 wave/second

Relating Wavelength and

Frequency

• We can write a mathematical expression that relates frequency and wavelength.

• c = !"

• c is the speed of light, ! is the wavelength, and " is the frequency.

• Since the speed of light is the same for all forms of EMR, the product of wavelength and frequency is constant.

• Wavelength and frequency are inversely proportional.

The Photoelectric Effect

• Wave theory could not explain everything involving the interactions between light and matter.

• One particular phenomenon that scientists were perplexed about was the photoelectric effect.

• The photoelectric effect refers to the emission of electrons from a metal when light shines on a metal.

The Photoelectric Effect

• The central question surrounding the photoelectric effect focused on the frequency of the light that hits a metal.

• Particle theorists believed that there was a minimum frequency of light needed to remove electrons.

• Wave theorists believed that any frequency of light would knock loose electrons.

Solution to the

Photoelectric Effect Problem

• 1900: German physicist Max Planck proposes a partial solution to the photoelectric effect.

• Planck believes that hot objects give off EMR in small packets called quanta.

• A quantum is the minimum amount of energy that can be gained or lost by an atom.

Max Planck 1858 - 1947

Planck’s Constant

• Planck finds a relationship that exists between quanta and the frequency of radiation.

• E = h"

• E (energy in joules), " (frequency), and h (Planck’s constant)

• h = 6.626 x 10-34 J･s

Einstein’s Solution

• 1905: Albert Einstein begins to expand on Planck’s idea about quanta.

• Einstein proposes that EMR has a wave-particle duality.

• He thought that since light and other forms of EMR can be thought of as waves, then EMR can also be thought of a a stream of particles.

• These particles were called photons.

Albert Einstein 1879 - 1955

Photons, Photons, Photons

• Photons are particles of EMR that have zero rest mass and a quantum of energy.

• Planck’s equation can be rewritten in terms of a relationship between the energy of a photon and its frequency.

• Ephoton = h"

• Einstein concluded that in order for an electron to be ejected from a metal, the electron must be struck by a photon with a minimum amount of energy.

•

Light as Particles

• The minimum amount of energy needed is tied to the minimum frequency of the light needed.

• Different elements require different minimum frequencies to exhibit the photoelectric effect.

• Einstein wins a Nobel Prize in Physics in 1924 due to his work on the photoelectric effect.

The Hydrogen-Atom Line-

Emission Spectrum

• Electrons can gain or lose energy.

• Electrons can be in the ground state or the excited state.

• The ground state of an electron is the lowest energy state for an atom and is the most stable.

• The excited state of an electron is any energy state higher in potential energy than the ground state.

The Hydrogen-Atom Line-

Emission Spectrum (continued)

• When scientists passed an electric current through a vacuum containing hydrogen gas at low pressure, the excited hydrogen atoms had a pinkish glow.

• When this light was passed through a prism, the light split into specific color bands.

• This separation is called the line emission spectrum of hydrogen.

Line Emission Spectrum

Ground State vs. Excited State

• In order for an atom (or electron) to reach an excited state from the ground state, energy must be added.

• Once an atom (or electron) reaches an excited state and begins to return to the ground state or lower energy state, the atom releases a photon of energy.

• This photon has an energy that is equal to the energy difference between the two energy states.

• Ephoton = E2 -E1 or Einitial - Efinal

Ground State vs. Excited State

Bohr Model of the Atom

• 1913: Danish physicist Niels Bohr proposes a model of the atom based on electrons and photon emission.

• Main idea: electrons revolve around the nucleus in circular paths called orbits.Niels Bohr

1885 - 1962

Bohr Model of the Atom

• The atom and electrons are in the lowest energy state (ground state) when the electrons are in orbits closest to the nucleus.

• The energy of the electron increases as the distance between the orbit and nucleus increases.

• In order to move from orbit to orbit, a photon must be released or absorbed.

The Quantum Model of the Atom

• 1924: French scientist Louis de Broglie suggests that electrons be considered as waves confined to the space around an atomic nucleus

Louis de Broglie 1892 - 1987

The Quantum Model of the Atom

• 1927: German physicist Werner Heisenberg tries to detect electrons by using their interactions with photons.

• Since photons have about the same energy as electrons, finding a specific electron with a photon would cause the electron to veer off course.Werner Heisenberg

1901 - 1976

The Quantum Model of the Atom

• Due to this fact, Heisenberg deduces that there is always an uncertainty in attempting to find an electron.

• Heisenberg Uncertainty Principle (HUP): It is impossible to know both the position and velocity of an electron.

The Quantum Model of the Atom

• 1926: Austrian physicist Erwin Schrödinger uses the wave-particle duality to write an equation that treats electrons as waves.

• Pairing of the Schrödinger Wave Equation (SWE) with the HUP, leads to the foundation of modern quantum theory.

Erwin Schrödinger 1887 - 1961

The Quantum Model of the Atom

• When the SWE is solved, the results are called wave functions.

• Wave functions can only give the probability of finding an electron at a given point.

• Due to wave functions, we know that electrons do not travel in circular orbits. Instead, electrons reside in certain regions called orbitals (3-D regions about the nucleus that indicate the probable location of an electron).