Question

Figure \(5.14\) shows thrce energy-level transitions that produce three spectral lines in a spectroscope. Note that the distance between the \(n=1\) and \(n=2\) levels is greater than the distance between the \(n=2\) and \(n=3\) levels. Would the number of spectral lines produced change if the distance between the \(n=1\) and \(n=2\) levels were exactly the same as the distance between the \(n=2\) and \(n=3\) levels?

Short answer

The number of spectral lines would remain the same.

Step-by-step solution

Understanding Energy Level Transitions

Spectral lines are produced when electrons transition between energy levels in an atom. Each transition corresponds to a specific difference in energy, resulting in a unique spectral line.

Analyzing Current Scenario

In the given scenario, there are three energy levels (=1, n=2, n=3"). The transitions between them, such as from \(n=3\) to \(n=2\), \(n=3\) to \(n=1\), and \(n=2\) to \(n=1\), produce three distinct spectral lines.

Exploring Hypothetical Scenario

If the distance between the \(n=1\) and \(n=2\) levels were the same as between the \(n=2\) and \(n=3\) levels, the energy difference for each transition would not affect the number of spectral lines. The factors influencing spectral lines are the number of transitions possible, not the energy distance.

Conclusion of Theoretical Analysis

The number of transitions, which is three, dictates the number of spectral lines, not the distance between the energy levels. Therefore, the number of spectral lines would remain unchanged in this hypothetical scenario with equal distances between levels.

Key concepts

Energy Level Transitions

Energy level transitions occur when an electron moves between different energy levels in an atom. These energy levels are quite similar to rungs on a ladder. Electrons can jump from one rung to another, either moving up or down.
An upward transition, where an electron absorbs energy, moves it to a higher energy level. When it returns to a lower energy level, it releases energy in the form of light. This process creates spectral lines that we can observe using special tools.
Each transition corresponds to a precise energy difference between the starting and ending energy levels. This determines the color and properties of the light emitted.

Spectroscope

A spectroscope is an instrument used to observe spectral lines. It separates light into its different wavelengths, much like a prism or a rainbow.
These wavelengths appear as lines of different colors, and each line corresponds to a specific electron transition within an atom.

• Spectroscopes are essential tools in understanding atomic behavior.
• They help scientists analyze the composition of distant stars by observing their light.
• This analysis provides valuable information about the chemical elements present in the star.

Electron Transitions

Electron transitions are movements of electrons between orbitals or energy levels within an atom. These transitions create the characteristic spectral lines.
A higher energy level transition results in a spectral line in the ultraviolet region, while a lower energy transition appears in the visible light region.

• Larger energy jumps produce higher frequency light, like ultraviolet.
• Smaller energy jumps result in lower frequency light, like red light in the visible spectrum.

Energy Difference

The energy difference between levels is critical in determining the frequency and wavelength of the emitted light.
The greater the energy difference, the higher the frequency and the shorter the wavelength of the light produced.
This principle explains why each element produces a unique pattern of spectral lines, known as its emission spectrum.

• Energy levels in an atom are not equally spaced. Closer energy levels produce light with longer wavelengths.
• Changes in energy levels correspond to specific colors of light in the spectrum.

Atomic Spectra

Atomic spectra are the fingerprints of elements. They are unique patterns of light created by electron transitions within an atom.
Each element has a distinct spectrum due to its unique energy level structure.

• These spectra are instrumental in identifying elements in distant stars and galaxies.
• They are also used to determine the physical conditions and compositions of stars.
• Atomic spectra not only tell us about energy transitions but also about the history and workings of the universe.