Question

In the emission spectrum from hydrogen gas, what type of energy is released when electrons drop from the fifth to the fourth energy level?

Short answer

Infrared energy is released when electrons drop from the fifth to the fourth energy level in hydrogen.

Step-by-step solution

Understand the Context

In an emission spectrum, particular energies are released when electrons transition between energy levels in an atom. For hydrogen, when an electron jumps from a higher energy level to a lower one, it emits energy in the form of electromagnetic radiation, typically known as a photon.

Identify the Energy Levels Involved

In this problem, electrons drop from the fifth energy level (\( n=5 \) ) to the fourth energy level (\( n=4 \) ). The energy levels of an electron in a hydrogen atom are quantized and can be described by the quantum number \( n \).

Recall the Spectral Series

The spectral series for hydrogen are categorized based on the lower level the electron drops to. The electron is transitioning from \( n=5 \) to \( n=4 \), which is part of the Brackett series. The Brackett series involves transitions where electrons drop to the \( n=4 \) level, releasing infrared radiation.

Confirm Energy Release Type

Since the electron transition from \( n=5 \) to \( n=4 \) falls under the Brackett series, which is characterized by the emission of infrared radiation, the energy released is infrared.

Key concepts

Electromagnetic Radiation

Electromagnetic radiation is a fundamental phenomenon that encompasses a wide range of energy forms, from radio waves to gamma rays. It is the mechanism by which energy and information travel through space. In simpler terms, it's like a wave that can travel through either a vacuum or a medium like air, carrying energy.
In the context of atomic transitions, such as those in a hydrogen atom, when an electron falls from a higher energy level to a lower one, it releases energy. This energy is emitted as electromagnetic radiation, often in the form of a photon. The type of electromagnetic radiation released depends on the difference in energy levels.

• The larger the energy difference, the shorter the wavelength of the radiation (e.g., ultraviolet).
• Conversely, smaller energy differences result in longer wavelengths, such as infrared radiation.

This concept is vital in understanding how elements, like hydrogen, produce different spectral lines and how these lines relate to electron transitions.

Quantum Number

Quantum numbers are numerical values that describe the quantized nature of electrons in an atom. These numbers provide a way to visualize the quantum state of an electron and its probable location in relation to the nucleus.
The principal quantum number \(n\) is one of the most important numbers as it denotes the energy level of an electron. For example, in hydrogen's emission spectrum, they show the specific levels between which an electron moves.

• Electrons in higher quantum number levels \(n\) have more energy and are further from the nucleus.
• As electrons transition to a lower \(n\), they release energy in the form of electromagnetic radiation.

Understanding these numbers is crucial for predicting the type of radiation emitted and for identifying the spectral series associated with specific electron transitions.

Brackett Series

The Brackett series is a group of spectral lines corresponding to electron transitions to the fourth energy level \(n=4\) in a hydrogen atom. This series is part of the hydrogen spectra which includes the transitions involving infrared radiation emission.
When an electron transitions to the fourth energy level from higher levels such as \(n=5\), it results in the emission of infrared light. The Brackett series thus is visible in the infrared range, making it crucial in infrared spectroscopy.

• The Brackett series serves as an essential tool in astrophysics for identifying star compositions through the analysis of emitted infrared radiation.
• Understanding these transitions helps scientists determine the physical properties of stellar and interstellar objects.

Knowing about the Brackett series and its role in the large scheme of atomic transitions can provide deeper insights into the behavior of electrons and the light they emit.