Question

Suppose an electron falls from \(n=4\) to its ground state, \(n=1\). Which of the following effects is most likely? A. A photon is absorbed. B. A photon is emitted. C. The electron gains velocity. D. The electron loses velocity.

Short answer

B. A photon is emitted.

Step-by-step solution

- Identify the Initial and Final States

Determine the energy levels involved in the transition. Here, the electron falls from the fourth energy level (=4) to the ground state (=1).

- Understand Energy Transitions

Recognize that when an electron moves from a higher energy level to a lower one, energy is released in the form of a photon.

- Apply the Concept of Photon Emission

Since the electron is falling to a lower energy state, it will emit energy. This emission takes place in the form of a photon.

- Evaluate the Options

Compare each option to the established concept: A. A photon is absorbed (incorrect, as absorption would occur if the electron were moving to a higher state). B. A photon is emitted (correct, as this matches the concept of energy release in the form of a photon). C. The electron gains velocity (incorrect, as electron transitions are energy-related, not velocity-related). D. The electron loses velocity (incorrect, as velocity change is not the primary effect in quantum energy level transitions).

Key concepts

photon emission

When an electron transitions from a higher energy level to a lower one, it releases energy. This energy is emitted in the form of a photon, a particle of light. In the given exercise, the electron falls from the fourth energy level to the ground state. The result is the emission of a photon. This process is a fundamental concept in quantum mechanics.

Photons carry the energy difference between the two levels. The energy of the emitted 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 emitted photon.

Understanding photon emission helps explain how electrons behave in atoms and how light is produced at the atomic level. Electronic transitions resulting in photon emission are the basis for the light we observe from stars, including our sun.

energy levels

Atoms have distinct energy levels where electrons reside. These levels are often denoted by the principal quantum number \(n\). For instance, in the exercise, the electron moves from \(n=4\) to \(n=1\). Each energy level corresponds to a specific amount of energy. Higher levels are at higher energy states.

When an electron jumps between these levels, it must absorb or emit energy equivalent to the difference between the two levels. For an electron to fall from a higher level to a lower one, it must release energy. This energy is ejected as a photon.

The concept of energy levels is key to understanding atomic structure and behaviors such as:

• Spectral lines in both absorption and emission spectra
• Chemical bonding and molecular structure
• The functioning of lasers and other light-emitting devices

Properly grasping energy levels allows for a better understanding of a wide range of physical and chemical phenomena.

quantum mechanics

Quantum mechanics is the branch of physics that deals with the behavior of particles at atomic and subatomic scales. Unlike classical physics, quantum mechanics describes quantities such as energy and angular momentum in discrete values called 'quanta'.

One of the main principles of quantum mechanics is that particles like electrons exist in specific energy levels or 'quantized' states. When an electron transitions from one state to another, it does so by absorbing or emitting a photon. This is a quantized action, meaning it happens in fixed, discrete amounts.

The principles of quantum mechanics can be summarized as follows:

• Electrons occupy specific energy levels.
• Transition between levels involves absorption or emission of quanta (photons).
• Properties like energy, momentum, and angular momentum are quantized.

Quantum mechanics explains not just electron transitions in atoms but also phenomena like:

• Superposition and entanglement
• The dual nature of particles and waves
• The uncertainty principle

By studying these principles, one can gain a deeper understanding of the fascinating and often counterintuitive behaviors that occur at the quantum level.