Question

How many photons of light are emitted for each of the following? (a) \(1 \mathrm{e}^{-}\) drops from energy level 3 to 1 (b) \(1 \mathrm{e}^{-}\) drops from energy level 3 to 2

Short answer

For both (a) and (b), one photon is emitted for each electron transition.

Step-by-step solution

Identify the energy levels

First, determine the energy levels involved in each transition. For part (a), the transition is from energy level 3 to 1. For part (b), the transition is from energy level 3 to 2.

Understand photon emission

A photon is emitted when an electron transitions from a higher energy level to a lower energy level. The energy of the emitted photon corresponds to the difference between the initial and final energy levels.

Analyze the number of photons emitted

In both parts (a) and (b), the transitions involve a single electron dropping between energy levels. Each transition of an electron from a higher to a lower energy level results in the emission of exactly one photon.

Conclusion of transitions

For part (a), the electron transition from level 3 to 1 emits one photon. Similarly, for part (b), the transition from level 3 to 2 also emits one photon.

Key concepts

Photon Emission

In the world of quantum mechanics, photons play a crucial role when electrons change their energy levels. A photon is a particle of light that is released when an electron transitions from one energy level to another. This transition is not random but follows a specific process. When an electron falls from a higher energy level to a lower one, it loses energy.
For an electron dropping from level 3 to 1, it loses a significant amount of energy, which is released in the form of a photon. The same principle applies for an electron moving from level 3 to level 2, although the energy lost and thus the photon's energy is different because the gap between these specific levels is smaller.
The key takeaway is:

• Each transition results in the release of exactly one photon.
• The energy of the photon emitted is precisely equal to the energy difference between the two levels involved in the transition.

Energy Levels

Energy levels can be understood as the steps in a quantum staircase that electrons move up and down on. Think of each energy level as a distinct rung on a ladder that electrons occupy. In atoms, these levels are determined by the configuration of electrons around the nucleus, quantified by a principal quantum number (n).
The farther an electron is from the nucleus, the higher its associated energy level. Higher energy levels correspond to greater amounts of energy. For example, an electron at energy level 3 has more energy than one at level 2 or 1.
When electrons drop to a lower rung, such as from level 3 to 1, they release energy because they are moving to a state of lower potential energy. This change, the difference between these energy levels, determines the energy of the emitted photon.

• Higher energy levels = more energy
• Lower energy levels = less energy
• Transitions release energy as photons

Electron Transitions

Every transition of an electron between energy levels is a fascinating and fundamental process in atomic physics. When an electron moves, it can either absorb or release energy in the form of light, known as a photon, depending on the direction of its movement.
When it falls to a lower energy level, like from level 3 to either level 1 or 2, it emits a photon. This is because moving to a lower level means it must lose some of its energy. The specific amount of energy it loses depends on the difference between the two levels.
Understanding these electron transitions gives us insight into:

• The behavior and properties of atoms.
• The emission spectra of different substances, which are essentially fingerprints that can be used to identify different elements and compounds.
• How light is produced at a quantum level.

These transitions are vital for applications ranging from spectroscopy to the development of lasers and LEDs.