Suppose an atom has three energy levels, specified in arbitrary units as \(10,7,\) and \(5 .\) In these units, which of the following energies might an emitted photon have? (Select all that apply.) a. 3 b. 2 c. 5 d. 4

When an atom transitions from a higher energy level to a lower energy level, it emits a photon. The photon carries away the difference in energy between these two levels. This process is known as photon emission.

For instance, in our exercise, the atom can transition between energy levels 10, 7, and 5. Thus, when the atom moves from an energy level of 10 to 7, it emits a photon with an energy equivalent to the difference between these levels. This energy difference is 3 arbitrary units.

Because photon emission is tied to specific amounts of energy, we can calculate the exact energy of the emitted photons by examining the energy transitions. This concept forms the backbone of understanding atomic spectra and how atoms release energy.

Energy transitions occur when an electron in an atom moves between different energy levels. These changes are quantized, meaning only certain energy values are allowed. In our exercise, the energy levels are 10, 7, and 5 arbitrary units.

Possible energy transitions can be:

• 10 to 7
• 10 to 5
• 7 to 5

Each of these transitions will emit a photon whose energy corresponds to the difference in energy between the levels involved. For example, the transition from 7 to 5 will emit a photon with an energy of 7 - 5 = 2 units.
By analyzing these transitions, we can determine which photon energies are possible, explaining why in our exercise, we have the energies 3, 2, and 5 as potential emitted photon energies.

Quantum mechanics is the branch of physics that studies particles at the smallest scales - the atomic and subatomic levels. It provides a framework for understanding the behavior of electrons in atoms and the quantized nature of energy levels.

In quantum mechanics, an atom's electrons can only occupy specific energy levels. These levels are quantized, not continuous. When an electron transitions between these levels, it must absorb or emit a photon with an energy exactly equal to the difference between the initial and final levels.
Due to these rules, quantum mechanics allows us to predict the specific energies associated with photon emission, which is fundamental to solving our exercise. The precise counting of the energy differences, and resulting photon energies (3, 2, and 5 units), is based on these underlying quantum principles.

To understand photon emission in the context of atomic energy levels, we need to perform energy calculations. These calculations are straightforward once the possible energy transitions are identified.

Here's a step-by-step breakdown:

• Identify all possible transitions: from 10 to 7, from 10 to 5, and from 7 to 5.
• Calculate the energy differences for each transition. This gives us: 10 - 7 = 3 units, 10 - 5 = 5 units, and 7 - 5 = 2 units.
• Compare the calculated energy differences with the given options in the exercise (3, 2, 5, 4).
• Conclude which energies can be emitted photons: in our example, these are 3, 2, and 5 units.

By methodically following these steps, it becomes clear which photon energies are feasible based on the given energy levels, making complex quantum behavior understandable.