The Archmage's Ruminations

What your Glow-in-the-Dark Frisbee and your Microwave have in Common

Blogmaster Helen Cothrel,

Have you ever watched a glow-in-the-dark Frisbee soar through the inky blackness of night and wondered, “How does this majestic beast glow with such vigor?” Perhaps you then returned to your home and microwaved yourself a couple dozen pizza pockets . Would it surprise you that the function of both of those things can be explained by the same idea in physics? Don’t fear! I promise I won’t be throwing any math at you. You may see something scary, but I’ll explain everything so no one gets left in the dark.

Let’s consider a molecule. A molecule is a unit of atoms which are held together with chemical bonds. I’m not going to go into the details of bonding, but essentially it comes down to the arrangement of electrons (negatively charged particles that make up part of atoms) among the atoms. Also, for our purposes, let’s consider it a molecule of a gas.

A molecule of a gas has energy (no surprises there, right?). The total energy of the molecule can be separated into four types. These are as follows:

  1. Translational energy from the motion of the whole molecule through space. This is the same kind of energy a ball bouncing around has.
  2. Rotational energy from the molecule rotating about its center of mass (for a simple molecule as pictured below, think of rotating a dumbbell).
  3. Vibrational energy, which is due to the vibration of the atoms that make up the molecule (for a molecule like the one below, think of two balls attached on either side of a spring).
  4. Electronic energy from atomic interactions (interactions between electrons and other pieces of the atoms making up the molecule).

The breakdown of molecular energy. Image found here:

I am going to focus on the rotational and vibrational energies.

The rotational energy is dependent on two things: the angular momentum of the molecule and the molecule’s moment of inertia. The angular momentum is pretty much just a representation of the angular velocity, which is just how fast the molecule is rotating. The moment of inertia is a quantity determined by the physical properties of the molecule (specifically, its mass and its radius).

The important thing is that the angular momentum is “quantized;” this means it can only have certain values and it can only change in steps. Since the rotational energy is dependent on the angular momentum, it follows the same rules. If it helps to know, a “quantum” is a packet of energy, so the energy can only change by absorbing or emitting packets of energy. That means there are “allowed” values for the energy to have.

To consider the vibrational energy, it is helpful to use an analogy of springs. We can think of the bonds that are holding the molecule’s atoms together as springs. In a simple molecule like the one above, we are talking about something that looks like this:

A model of the spring analogy. Image here:

The vibrational energy breaks down to be dependent on the strength of the bonds between the atoms and the mass of the molecule. It turns out, the vibrational energy is also quantized! So both the vibrational and rotational energies can only change in steps, by absorbing or emitting packets of energy.

But why does this matter? Well, in many cases, the energy being absorbed or emitted by the molecules is electromagnetic energy. You’ve probably seen a picture of the “electromagnetic spectrum” before, but here’s a refresher:

The electromagnetic spectrum. Source:

But why does THIS matter? Well, we see the effects of this is countless ways. For example, the greenhouse effect can be explained by this knowledge. Carbon dioxide, which can be found in our atmosphere, doesn’t absorb visible light from the sun. It’s not “allowed” based on the vibrational and rotational energies (which can only change in very specific steps). This visible light then hits the surface of the Earth, which does absorb the energy.

The Earth warms up from absorbing all of this energy from the sun, and, in turn, emits infrared radiation. If you’ve ever seen an infrared camera or photos before, you may know that infrared is essentially heat. The infrared radiation that the warming Earth is giving off is “allowed” to be absorbed by the carbon dioxide in the atmosphere, so it is. This combination of effects raises the temperature of the Earth and the atmosphere.

Your household microwave works based on the same ideas of quantum physics. Microwaves can be absorbed by an important molecule which can be found in food: water. Your microwave barrages food with microwaves, the water molecules in the food absorb the energy and go nuts, and the food heats up.

Finally, some materials can absorb energy in the form of a photon, and then emit a photon shifted to a different wavelength (wavelength determines the color of light). This effect explains how we have some items that “glow-in-the-dark.” Some materials will absorb photons and then emit shifted photons after a time delay. So when the glow of your favorite watch, or shirt, or Frisbee or anything lingers in the darkness of a movie theater, you can sit comfortably knowing that it is brought to you by the wonders of quantum physics.

Source: Pretty much all of my knowledge in this comes from the book Modern Physics, 3rd edition, Serway/Moses/Moyer.

Thoughts? Questions? Leave a comment!


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