# Chapter 2.1: Wave - Particle Duality

 Prince George's Community College General Chemistry for Engineering CHM 2000 Unit I: Atoms      Unit II: Molecules     Unit III: States of Matter     Unit IV: Reactions     Unit V: Kinetics & Equilibrium Unit VI: Thermo & Electrochemistry     Unit VII: Nuclear Chemistry

Learning Objective

• To understand the wave–particle duality of matter.

Sitting at your computer, moving the mouse you can see the cursor move. In a similar way if someone tosses you a ball you can anticipate where it will be and catch it. If you catch the ball you can feel the shape in your hands. We could use a ruler or a caliper to measure the size of the ball. This is all obvious.

When we move to the atomic scale things are not obvious, in fact, since we have no experience on that scale, things will be quite confusing. For example, think about how you see the ball. Light whose wavelength is between 400 nm (blue) and 700 nm (red) bounces off the ball into your eye. The size of an atom is only about 0.1 nm. Using visible light, you would never be able to locate a single atom because the wavelength of the light would be thousands of times larger. Some might bounce off the atom into your eye but locating where it bounced could only narrow the location of the atom to ~500 nm or so.

Well, what if we used light with a 0.1 nm wavelength. You should remember from Introduction to Engineering that the wavelength of light is related to its frequency by

$$c=\lambda \nu \tag{2.1.1}$$

where c is the velocity of light in a vacuum, 3 x 108 cm/sec. Thus the frequency of 0.1nm light is 3.00 x 1018 Hz. At this point we will introduce a basic foundation of quantum mechanics, that the energy of a light particle, called a photon, is related to it's frequency by

$$E=h\nu \tag{2.1.2}$$

where h = 6.626 x 10-34 J-s, is Planck's constant. The energy of the photon we need to locate the atom is 2.00 x 10-15 J.

The simplest atom is Hydrogen, which consists of an electron bound to a proton. The energy holding the electron is 2.18 x 10-18​ J. Another basic principle of quantum mechanics is that the photon can act like a particle and when it hits the electron can cause it to move. Our 0.1 nm photon would simply blow the electron in the Hydrogen atom away. So we might know where the hydrogen atom was when the photon hit it, but we would have no idea where it would be blasted to after the photon hit it.

Measurement of the size of the atom poses similar issues, what can be used as a ruler? Does the atom have a sharp, well defined edge that we could measure?

The answer is no. What quantum mechanics teaches us is that every object has properties that are particle like and properties that are wave like. Massive objects (remember the ball) are more particle like. This includes atomic nucleii, which compared to the electrons are very heavy. Light electrons, on the other hand, have significant wavelike properties.

Although we still usually think of electrons as particles, the wave nature of electrons is employed in an electron microscope, which has revealed most of what we know about the microscopic structure of living organisms and materials. Because the size of electrons is much smaller than the wavelength of a beam of visible light, this instrument can resolve smaller details than a light microscope can (Figure 2.4.1 ).

Figure 2.4.1 A Comparison of Images Obtained Using a Light Microscope and an Electron Microscope Because of their shorter wavelength, high-energy electrons have a higher resolving power than visible light. Consequently, an electron microscope (b) is able to resolve finer details than a light microscope (a). (Radiolaria, which are shown here, are unicellular planktonic organisms.)

Our approach to quantum mechanics will be to present a few simple facts about the properties of electrons in atoms from which we can build up the properties of the atoms. A more complete discussion will occur in General Physics. The goal is to provide you with enough information about the properties of atoms (and then molecules) that you can understand their chemistry, without getting bogged down in the historical and mathematical background.

What can we say about the properties of an electron in an atom. Surprisingly we can say exactly what the energy of the electron is. While we cannot say where the electron is or will be, we can find the probability of finding the electron at any point in space. This information is contained in what we call the wave function which will be discussed in the next section.

## Summary

The modern model for the electronic structure of the atom is based on recognizing that an electron possesses particle and wave properties, the so-called wave–particle duality.

## Key Takeaway

• An electron possesses both particle and wave properties.

## Contributors

• Anonymous

Modified by Joshua Halpern, Scott Sinex and Scott Johnson