Question

In the Bohr model, how many photons are emitted when an electron moves directly from the \(n=5\) to the \(n=2\) orbit?

Short answer

The electron emits one photon when it transitions directly from the \(n=5\) to the \(n=2\) orbit in the Bohr model.

Step-by-step solution

Understand the Bohr Model

In the Bohr model, electrons orbit the nucleus in specific energy levels. When an electron moves from a higher energy level to a lower one (e.g., from \(n=5\) to \(n=2\)), it emits energy in the form of a photon.

Determine the number of transitions

In this case, the electron moves directly from \(n=5\) to \(n=2\). This is considered a single transition, even though it spans multiple energy levels. This is because the electron did not stop at intermediate levels (\(n=3\) and \(n=4\)), but transitioned directly from \(n=5\) to \(n=2\). Thus, only one photon is emitted.

Final Answer

The electron emits one photon as it transitions directly from \(n=5\) to \(n=2\) in the Bohr model.

Key concepts

Photon Emission

When an electron changes energy levels within an atom, it results in the emission or absorption of energy in the form of a photon. A photon is a particle representing a quantum of light or electromagnetic radiation. It's the basic unit that carries energy, and its creation or destruction signals a change in the energy state of the electron. In the context of the Bohr model:

- A photon is emitted when an electron moves from a higher energy level to a lower one.
- Each emitted photon has a specific energy equal to the difference between the two energy levels involved in the transition.
- The energy of a photon can be calculated using the formula \(E = hf\), where \(E\) is the energy, \(h\) is Planck's constant, and \(f\) is the frequency of the photon.

Photon emission is a fundamental process that explains how different wavelengths of light are produced when electrons in atoms transition between different energy states. This explains phenomena such as the emission spectra of elements, which are essentially their unique light "fingerprints.”

Electron Transition

Electron transition refers to the movement of an electron between energy levels or orbits within an atom. In the Bohr model, these transitions are quantized, meaning they occur in discrete steps rather than continuously.

- Each orbit or energy level is designated by a principal quantum number, \(n\).
- When an electron transitions from a higher energy level (like \(n=5\)) to a lower one (like \(n=2\)), this change is called an electron transition.

For an electron to transition, it must gain or lose energy. When moving to a higher energy level, the electron absorbs energy, typically from a photon. Conversely, when moving to a lower energy level, it emits energy in the form of a photon. Bohr's model uniquely identifies each possible transition by its specific energy difference, which defines the energy, frequency, and wavelength of the emitted or absorbed photon.

This concept helps to explain why atoms emit or absorb light at specific wavelengths, contributing to the larger theory of quantum mechanics and our understanding of atomic structure.

Energy Levels

Energy levels in the Bohr model represent the set positions where electrons can exist around an atom's nucleus. These are sometimes referred to as "shells" or "orbits." Understanding energy levels is essential for grasping how electrons behave and how they affect chemical reactions and photon emission.

- Each energy level corresponds to a particular amount of energy, characterized by the principal quantum number \(n\).
- Energy levels are discrete, meaning electrons can only exist in specific levels without occupying the space in between.
- The further an energy level is from the nucleus, the higher its energy. For example, \(n=5\) has a greater energy than \(n=2\).

When electrons "jump" between these levels, they gain or lose a quantifiable amount of energy. The transition from one level to another directly influences whether energy is absorbed or emitted, which in turn dictates whether an electron's shift will result in the absorption or emission of a photon. These transitions are key to understanding an atom's interaction with electromagnetic radiation and form the basis of numerous applications in chemistry and physics, such as spectroscopy.