The Development of aNew Atomic Model

The Rutherford model of the atom was an improvement over previous models, but it was incomplete.

J. J. Thomson’s “plum pudding” model, in which electrons are surrounded by a soup of positive charge to balance the electron’s negative charge, like negatively-charged “plums” surrounded by positively charged “pudding”.

It did not explain how the atom’s negatively charged electrons are distributed in the space surrounding its positively charged nucleus.

In the early twentieth century, a new atomic model evolved as a result of investigations into the absorption and emission of light by matter.

The studies revealed a relationship between light and an atom’s electrons.

Before 1900, scientists thought light behaved solely as a wave. This belief changed when it was later discovered that light also has particle-like characteristics.A quick review of these wavelike properties follows.

Properties of Light• Visible light is a kind of electromagnetic radiation

(form of energy that exhibits wavelike behavior as it travels through space). Other examples include X-rays, ultraviolet and infrared light, microwaves, and radio waves.

• The electromagnetic spectrum consists of all types of electromagnetic radiation.

Electromagnetic Spectrum

• All forms of electromagnetic radiation move at a speed of 3.0 x 108 m/s through air.

• Wavelength – λ (m, cm, or nm) and frequency – ν (wave/second) are measureable properties of wave motion. One wave/second is called a hertz (Hz).

• The relationship between wavelength (λ) and frequency (ν) is c = λν where c = speed of light.

Wavelength and Frequency

In the early 1900s, scientists conducted two experiments involving interactions of light and matter that could not be explained by the wave theory of light.

One experiment involved a phenomenon known as the photoelectric effect.

Photoelectric Effect• The photoelectric effect refers to the emission of

electrons from a metal when light shines on the metal.

Light may cause electrons to be emitted from an electrode in a photocell. Long wavelength light does not have enough energy to cause the electron to escape, regardless of its intensity. When light of a shorter wavelength (higher energy) light strikes the electrode, electrons are released. The amount of current produced depends on the intensity of the light and the energy of the escaping electrons depends on the wavelength of the light.

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The wave theory of light predicted that light of any frequency could supply enough energy to eject an electron. Scientists couldn’t explain why the light had to be of a certain frequency in order for the photoelectric effect to occur.

The German physicist Max Planck proposed an explanation for the photoelectric effect.He proposed that a hot object does not emit electromagnetic radiation continuously, as would be expected if the energy emitted were in the form of waves.

• Max Planck proposed that objects emit energy in small, specific amounts called quanta (1900).

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

• The relationship between a quantum of energy and the frequency of radiation is illustrated by the following equation:

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

frequency in s-1 of the radiation emitted, and h is a physical constant now known as Planck’s constant.

• Einstein proposed that electromagnetic radiation has dual wave-particle nature (1905). These particles are called photons.• A photon is a particle of electromagnetic radiation

having zero mass and carrying a quantum of energy.

• In order for an electron to be ejected from a metal surface, the electron must be struck by a single photon possessing the minimum energy and frequency to knock it loose.• The energy of a particular photon depends on the frequency of

the radiation. Ephoton = hν

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Hydrogen Atom Line-Emission Spectrum

• The ground state is the lowest energy level of an atom. When it has higher potential energy an atom is in its excited state.

• When an excited atom returns to its ground state it gives off energy in the form of colored light. (Example: Neon lights.)

• When doing experiments with hydrogen gas, it was found that hydrogen atoms emit only specific frequencies of light.

• The fact that hydrogen atoms emit only specific frequencies of light indicated that the energy differences between the atom’s energy states were fixed.

• This suggested that the electron of a hydrogen atom exists only in very specific energy states (led to quantum theory).

Hydrogen’s Line Emission Spectrum

Bohr Model of the Hydrogen Atom

• Niels Bohr proposed a model of the hydrogen atom that showed that the electron can circle the nucleus only in allowed paths (orbits) (1913).

The Quantum Model of theAtom

Electrons as Waves• In the early 1900s, it was found through

experimentation that light could behave as both a wave and a particle (dual-wave particle of nature).

• In 1924 Louis de Broglie experimented to see if electrons have a dual-wave particle of nature as well.

• He found that electrons did.

The Heisenberg Uncertainty Principle• The idea of electrons having a dual wave-particle

nature troubled scientists. If electrons are both particles and waves, then where are they in the atom?

• Heisenberg’s idea involved the detection of electrons. Electrons are detected by their interaction with photons. Because photons have about the same energy as electrons, any attempt to locate a specific electron with a photon knocks the electron off its course.

• As a result, there is always a basic uncertainty in trying to locate an electron.

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

The Schrödinger Wave Equation

• In 1926, Austrian physicist Erwin Schrödinger developed an equation that treated electrons in atoms as waves.

• Schrödinger’s wave equation laid the foundation for the quantum theory (1926).

• The quantum theory describes mathematically the wave properties of electrons and other very small particles.

• The theory suggested that electrons do not travel in neat orbits, as Bohr’s model showed, but in regions called orbitals.

• An orbital is a three-dimensional region around the nucleus that indicates the probable location of an electron.

Atomic Orbitals and Quantum Numbers

• In order to describe orbitals, scientists use quantum numbers (specify the properties of atomic orbitals and the properties of electrons in orbitals).

• The first three quantum numbers indicate the main energy level, the shape, and orientation of the orbital.

• The fourth, the spin quantum number, describes the state of the electron.

• Basically, quantum numbers were devised as a way to describe where individual electrons are located in an atom.

Principal Quantum Number• The principal quantum number, symbolized by n,

indicates the main energy level occupied by the electron.

• Values of n are positive integers only (e.g., 1, 2, 3…).• As n increases, the electron’s energy and its average

distance from the nucleus increases.

Principal Quantum Number

Energy

n = 1

n = 2

n = 3

n = 4n = 5n = 6

Angular Momentum Quantum Number

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

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

• Sublevels in the atoms of the known elements are s-p-d-f.

Shapes of Orbitals

Magnetic Quantum Number• The magnetic quantum number, symbolized by m,

indicates the orientation of an orbital around the nucleus.

• Orbitals contain one or two electrons, never more.

Spin Quantum Number• The spin quantum number, has only two possible

values (+1/2, -1/2) which indicate the two fundamental spin states of an electron in an orbital.

• Electrons in the same orbital must have opposite spins.

• Possible spins are clockwise or counterclockwise.