Electronic Structure of Atoms

The Wave Nature of Light

Electrons hold the key to understanding why substances behave as they do. When atoms react it is their outer pars, their electrons, that interact.

We refer to the arrangements of electrons in atoms as their electronic structure.

• Number of electrons
• Where they can be found
• The energies they possess

Be warned!: electrons to not behave like anything we are familiar with in the macroscopic world

Much of our present understanding of the electronic structure of atoms has come from analysis of the light emitted or absorbed by substances

Electromagnetic radiation

• Carries energy through space (also known as radiant energy)
• Includes visible light, dental x-rays, radio waves, heat radiation from a fireplace
• Share certain fundamental characteristics
• All move through a vacuum at 3.00 x 10⁸ m/s ("speed of light")
• Have "wave-like" characteristics

• The number of complete wavelengths, or cycles, that pass a given point in 1 second is the frequency of the wave

(frequency=cycles/second)

Electromagnetic radiation has both electric and magnetic properties. The wave-like property of electromagnetic radiation is due to the periodic oscillations of these components.

We can assign a frequency and a wavelength to electromagnetic radiation

Because all electromagnetic radiation moves at the same speed (speed of light) wavelength and frequency are related

• If the wavelength is long, there will be fewer cycles passing a given point per second, thus the frequency will be low
• If the wavelength is short, there will be more cycles passing a given point per second, and the frequency will be high
• Thus, there is an inverse relationship between wavelength and frequency

• (frequency [nu] * wavelength[lambda]) is a constant (c)

What is the speed of a wave?

Imagine you are on the beach watching the ocean waves go by, and you want to know the speed of the waves. There is an island offshore with a palm tree that will serve as a convenient frame of reference. You count the number of waves that pass by the tree in one minute:

In this case, two peaks (two wavelengths) pass by the tree in one minute. Thus, the frequency is 2 wavelengths/minute. If we measure the distance between the peaks (i.e. the wavelength) we can determine the speed of the wave:

Speed of the wave = (distance between peaks) * (frequency)

= (wavelength) * (frequency)

The unit of length chosen to describe a particular wavelength is typically dependent on the type of electromagnetic radiation

The range of EM wavelengths is dramatic

• The wavelengths of gamma-rays (<0.1 Å) are similar to the diameter of atomic nuclei
• The wavelengths of some radio waves can be larger than a football field

Frequency

• Frequency is expressed in cycles per second, also known as hertz (Hz)
• Usually the dimension 'cycles' is omitted and frequencies thus have the dimension of s^-1

Sodium vapor lamps are sometimes used for public lighting. They give off a yellowish light with a wavelength of 589 nm. What is the frequency of this radiation?

frequency*wavelength = speed of light

frequency = speed of light/wavelength

= (3.00x10⁸ m/s)/(589x10^-9m)

= 5.09 x 10¹⁴ s^-1

= 5.09 x 10¹⁴ cycles per second or 5.09 x 10¹⁴ hertz

1996 Michael Blaber