Question

How many photons of light are emitted for each of the following? (a) \(100 \mathrm{e}^{-}\) drop from energy level 3 to 2 (b) \(100 \mathrm{e}^{-}\) drop from energy level 4 to 2

Short answer

100 photons are emitted for each scenario.

Step-by-step solution

Understanding the Electrons and Photons Relationship

When an electron drops from a higher energy level to a lower one, it emits a photon. The energy of the photon corresponds to the energy difference between the two levels. In this problem, you are asked to determine how many photons are emitted given a certain number of electrons dropping between specific levels.

Calculating Photons for Electrons from Level 3 to 2

Each electron dropping from energy level 3 to level 2 emits one photon. Since there are 100 electrons making this transition, the number of photons emitted is equivalent to the number of electrons: 100 photons.

Calculating Photons for Electrons from Level 4 to 2

Similarly, each electron dropping from energy level 4 to level 2 emits one photon. With 100 electrons making this transition, the number of photons emitted is also 100 photons.

Key concepts

Energy Levels

In physics, particularly in the quantum mechanics realm, **energy levels** refer to the discrete amounts of energy that an electron can have within an atom. These levels are often depicted as orbits or shells around the nucleus in a simplified model.

Each energy level corresponds to a particular state of energy with which an electron can be bound to an atom. An important feature is that these energy levels are quantized, meaning electrons can only exist in specific energy states and not between them. Think of these levels like rungs on a ladder - an electron can occupy a rung (energy level) but cannot exist between rungs.

• **Ground State**: Refers to the lowest energy level an electron can occupy.
• **Excited State**: Refers to any energy level higher than the ground state, where an electron can jump temporarily.

When an electron absorbs energy, it moves to a higher energy level or excited state. Conversely, when it loses energy, it falls back to a lower energy level and releases the excess energy often in the form of a photon.

Electron Transitions

**Electron transitions** are the movements of electrons between energy levels within an atom. These transitions are significant because they define a large portion of the atom's interaction with electromagnetic radiation.

For an electron to transition to a different energy level, it must either absorb or release energy equivalent to the difference between the two levels involved in the transition.

• **Absorption**: Occurs when an electron assimilates energy to jump to a higher energy level, which can come in the form of electromagnetic radiation or heat.
• **Emission**: Occurs when an electron falls to a lower energy level, releasing the absorbed energy, often as a photon.

During these transitions, only specific and quantized amounts of energy are exchanged. This characteristic is the foundation of understanding atomic spectra, where lines are formed based on the specific quantized energy changes that result from electron transitions.

Photons

A **photon** is a fundamental particle representing a quantum of light or other electromagnetic radiation. Photons are unique particles because they possess energy but have zero rest mass.

The energy of a photon is directly proportional to the frequency of the light and can be calculated using the formula:
\[ E = h \times f \]Where:

• \( E \) - energy of the photon,
• \( h \) - Planck's constant \( (6.62607015 \times 10^{-34} J\cdot s) \), and
• \( f \) - frequency of the electromagnetic wave.

Photons play a crucial role in the **electron transition** process. When an electron falls from a higher to a lower energy level, it releases the energy difference in the form of a photon.

This emission of photons can be observed as visible light or other forms of electromagnetic radiation, depending on the energy levels involved. This principle underpins many technologies, including lasers and photovoltaics, and is essential in understanding natural phenomena like auroras and the colors of fireworks.