# "Quantized Energy: Exploring 3 Bound States

• clutch12
In summary, the conversation discusses a scenario where a quantum object has three quantum states and emits electromagnetic radiation of three different energies (0.2 eV, 2.1 eV, and 2.3 eV) when excited. The conversation then goes on to ask for energy-level diagrams for the object and the possible transitions that produce the observed photons. It also mentions a scenario where the object is cooled down and a beam of light with a continuous range of energies is shone on it. The conversation also considers another possible set of energy levels and how it affects the observed photon energies. Finally, it discusses the use of absorption experiments to determine which energy-level scheme is correct.
clutch12

## Homework Statement

Suppose we have reason to suspect that a certain quantum object has only three quantum states. When we excite a collection of such objects we observe that they emit electromagnetic radiation of three different energies: 0.2 eV (infrared), 2.1 eV (visible), and 2.3 eV (visible).
(a) Draw a possible energy-level diagram for one of the quantum objects, which has three bound states. On the diagram, indicate the transitions corresponding to the emitted photons, and check that the possible transitions produce the observed photons and no others. When you are sure that your energy-level diagram is consistent with the observed photon energies, enter the energies of each level (K+U, which is negative). Enter ALL levels before submitting; all of the energies must be correct to be properly scored. The energy K+U of the ground state is -5 eV.

(b) The material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. Next a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. What photon energies in this beam of light are observed to be significantly reduced in intensity ("dark absorption lines")?

Energy of highest-energy dark line: eV
Energy of lowest-energy dark line: eV

(c) There exists another possible set of energy levels for these objects which produces the same photon emission spectrum. On an alternative energy-level diagram, different from the one you drew in part (a), indicate the transitions corresponding to the emitted photons, and check that the possible transitions produce the observed photons and no others. When you are sure that your alternative energy-level diagram is consistent with the observed photon energies, enter the energies of each level (K+U, which is negative). Enter ALL levels before submitting; all of the energies must be correct to be properly scored.

eV = energy of highest level (2nd excited state)
eV = energy of next highest level (1st excited state)
-5 eV = energy of ground state

(d) For your second proposed energy-level scheme, what photon energies would be observed to be significantly reduced in intensity in an absorption experiment ("dark absorption lines")? (Given the differences from part (b), you can see that an absorption measurement can be used to tell which of your two energy-level schemes is correct.)

Energy of highest-energy dark line: eV
Energy of lowest-energy dark line: eV

## Homework Equations

I don't think i need equations.

## The Attempt at a Solution

for part a, I was able to solve it by 2.3 from 2.1 and then subtracting 5 from 2.7
so my answers for a were -0.2 and -2.3

for b to d, i have no clue what I am doing wrong. I've been subtracting numbers and have been getting the wrong answers. Anyone have an idea why this is happening?

clutch12 said:
for part a, I was able to solve it by 2.3 from 2.1 and then subtracting 5 from 2.7
Why? 2.7 eV isn't even in the problem statement.

An energy level at -0.2 eV would produce a transition going from -0.2 eV to -5 eV, emitting and absorbing photons with 4.8 eV.

A three-level system only has three transitions, we have three transition energies so they must all occur. The highest energy difference (2.3 eV) will be between the ground state at -5 eV and the highest energy level, so this energy level must be at -5 V - (-2.3 eV) = -2.7 eV. The other one must be in between, which leads to two options: 0.2 eV above the ground state (at -4.8 eV) or 0.2 below the highest state (at -2.9 eV). Each position automatically puts it 2.1 eV away from the other state, as needed for the third transition. Just with the given information we can't distinguish between these cases, so one option is used for (a) and (b) and the other is used for (c) and (d).

## What is quantized energy?

Quantized energy refers to the concept that energy can only exist in discrete, specific amounts or levels. This is in contrast to the classical view of energy, which states that it can exist at any level.

## Why is quantized energy important?

Quantized energy is important because it helps us understand the behavior of particles at the atomic and subatomic level. It also plays a crucial role in various fields of science, such as quantum mechanics and atomic physics.

## What are the three bound states of quantized energy?

The three bound states of quantized energy are the ground state, the excited state, and the ionized state. The ground state is the lowest energy level that an electron can occupy, while the excited state is a higher energy level. The ionized state occurs when an electron is completely removed from its atom.

## How are the three bound states of quantized energy related?

The three bound states of quantized energy are related by the amount of energy required to move an electron from one state to another. For example, an electron can move from the ground state to the excited state by absorbing a specific amount of energy, and it can return to the ground state by releasing the same amount of energy.

## How does quantized energy impact our daily lives?

Quantized energy may seem like a complex concept, but it has a significant impact on our daily lives. For example, the quantized energy levels of atoms determine the colors we see, the wavelengths of light used in technologies such as lasers, and the chemical reactions that occur in our bodies. Without quantized energy, our world would look and function very differently.

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