CHAPTER 4: ARRANGEMENT OF

ELECTRONS IN ATOMS

The Development of a New Atomic Model The Rutherford model of the atom was

an improvement over previous models of the atom.

But, there was one major problem: If the electrons are negatively charged

and the nucleus was positively charged, then what prevented the electrons from being drawn into the nucleus?

Properties of Light

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

We later found that light also behaves as particles, but most of light’s properties can be attributed to its wave-like behavior.

Electromagnetic Radiation What is electromagnetic radiation

(EMR)? Answer: a form of energy that exhibits

wavelike behavior as it travels through space

Examples of EMR include X rays, UV light, microwaves, visible light and radio waves.

Electromagnetic Radiation (cont’d) When all forms of EMR are brought

together, the electromagnetic spectrum is formed.

All forms of EMR travel at the same speed through a vacuum at 3 x 108 m/s.

Electromagnetic Spectrum

Light as Waves

Light is repetitive in nature similar to waves.

Some of the most measurable properties of waves are wavelength and frequency.

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

Light as Waves (cont’d)

Wavelength can be measured in meters, centimeters, or nanometers.

The primary choice for wavelength is nanometers ( 1nm = 1 x 10-9 m).

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

Light as Waves (cont’d)

Light as Waves (cont’d) We can write a mathematical expression that

relates frequency and wavelength.

c = In the previous equation, 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. Therefore, wavelength and frequency are inversely proportional.

The Photoelectric Effect

Scientists conducted an experiment involving the interactions between light and matter that could not be explained by the wave theory.

This experiment revolved around the idea of the photoelectric effect.

Photoelectric effect refers to the emission of electrons from a metal when light shines on the metal.

The Photoelectric Effect (cont’d)

The remaining question surrounding the photoelectric effect dealt with frequency of light that struck the metal.

During the course of the experiment, no electrons were emitted if the frequency was below a certain minimum.

According to the wave theory of light, any frequency of light should have knocked loose an electron.

The Photoelectric Effect (cont’d)

Light as Particles

In 1900, German physicist Max Planck begins to explain the photoelectric effect.

His explanation was based on the emission of light by hot objects.

He proposed that hot objects did not continuously emit EMR, instead the released small, specific amounts of energy called quanta.

Light as Particles (cont’d) A quantum is the minimum amount of

energy that can be gained or lost by an atom.

Planck derived a relationship between a quantum and the frequency of radiation.

E = h E = energy (in joules), = frequency,

and h = Planck’s constant h = 6.626 x 10-34 Js

Light as Particles (cont’d) In 1905, Albert Einstein expands on

Planck’s idea about quanta. Einstein proposes that EMR has a

wave-particle duality. Since light and other forms of EMR can

be thought of as waves, then EMR can also be thought of as a stream of particles. These particles are called photons

Light as Particles (cont’d) Photons are particles of EMR that have

zero rest mass and a quantum of energy. We can rewrite the relationship between

energy and frequency in terms of photons. Ephoton = h From this equation, Einstein concluded

that in order for an electron to be ejected from the metal, it must be struck by one photon that has at least the minimum energy required.

Light as Particles (cont’d) So, the minimum amount of energy

needed is tied to the minimum frequency of the light needed.

Different elements required different minimum frequencies to undergo the photoelectric effect.

Einstein eventually wins Nobel Prize for Physics in 1924 due to this work.

The Hydrogen-Atom Line-Emission Spectrum Electrons can gain or lose energy as we

have previously discussed. Electrons can be in the ground state or

the excited state. The ground state is the lowest energy

state for an atom and it is the most stable. The excited state is any state in which the

atom has a higher potential energy than the electron’s ground state.

Hydrogen-Atom Line-Emission Spectrum (cont’d)

When scientists passed 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, it split into specific color bands.

This is called the line-emission spectrum of hydrogen.

Hydrogen-Atom Line-Emission Spectrum (cont’d)

Hydrogen-Atom Line-Emission Spectrum (cont’d)

Ground State vs. Excited State

In order to an atom (or electron) to get to the excited state from the ground state, energy has to be added.

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

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

Ephoton = E2 – E1 or Ei - Ef

Ground State vs. Excited State (cont’d)

Bohr Model of the Hydrogen Atom 1913- Danish physicist Niels Bohr

proposed an atomic model based on electrons and photon emission.

The Bohr model suggests that electrons circle the nucleus in circular paths called orbits.

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

Bohr Model of the Hydrogen Atom (cont’d) The energy of the electron increases

when the orbits are farther from the nucleus.

In order for electrons to move to another orbit, a photon of energy must be absorbed by the electron. This energy must equal the energy difference between the two orbits. (See the formula discussed during ground state vs. excited state)

Bohr Model of the Hydrogen Atom (cont’d) In order for an electron to move from an

state of higher energy to one of a lower energy, it must release a photon of energy equal to the difference between the two energy levels.

Representation of Bohr Model

The Quantum Model of the Atom Electrons as Waves 1924- French scientist Louis de Broglie

asks, “Could electrons have a dual wave-particle nature as well?”

De Broglie suggested that electrons be considered as waves confined to the space around an atomic nucleus.

The Quantum Model of the Atom (cont’d) The Heisenberg Uncertainty Principle

(HUP) 1927- German theoretical physicist

Werner Heisenberg decided to attempt to detect electrons by using their interactions with photons.

Since photon have about the same energy as electrons, finding a specific electron with a photon would knock the electron off course.

The Quantum Model of the Atom (cont’d) Because of this, there is always an

uncertainty in attempting to find an electron.

HUP: It is impossible to know both the position and velocity of an electron.

The Quantum Model of the Atom (cont’d) The Schrodinger Wave Equation (SWE) 1926- Austrian physicist Erwin

Schrodinger uses the wave-particle duality to write an equation that treats electrons as waves.

Pairing the SWE and the HUP together led to the foundation of modern quantum theory.

The Quantum Model of the Atom (cont’d) When the SWE is solved, the results are

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 indicates the probable location of an electron).