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Chapter 8: Problem 98

Draw an energy-level diagram that represents all the possible lines in the emission spectrum of hydrogen atoms produced by electron transitions, in one or more steps, from \(n=5\) to \(n=1\).

Short Answer

Expert verified
The energy-level diagram will be a vertical diagram with 5 horizontal lines. From top to bottom, the lines are marked from 5 to 1. Arrows are drawn from level 5 to represent possible transitions to lower levels until reaching level 1. This diagram will show all the possible lines in the emission spectrum of a hydrogen atom for transitions from the fifth energy level to the first, covering Lyman, Balmer, Paschen, Brackett and Pfund series.

Step by step solution

01

Understand Electron Transitions

Electrons in a hydrogen atom can move from one energy level to another. When an electron moves from a higher energy level to a lower one, it loses energy. This lost energy is emitted in the form of light, resulting in spectral lines. The energy difference between the levels determines the color (wavelength) of the light, thus different transitions cause different spectral lines. In this exercise, the electron is moving from higher energy level (n=5) to the lowest one (n=1).
02

Draw Energy-Level Diagram and Mark Levels

Draw a vertical diagram with horizontal lines denoting energy levels of the hydrogen atom. Each line represents a distinct energy level, so they should be labeled from bottom to top as 1, 2, 3, 4, and 5. Since the electron is moving from 5 to 1, the highest level in this case will be 5 and the lowest will be 1. The levels become closer together as they increase in number, reflecting the decreasing energy differences between them.
03

Indicate Transitions and Corresponding Spectral Lines

Now, start from level 5 and draw arrows representing possible transitions to lower levels till reaching level 1. Each of the transitions, whether it is direct (e.g., from n=5 to n=1) or in one or more steps (e.g., from n=5 to n=2, then to n=1) corresponds to a distinct line in the emission spectrum of hydrogen.
04

Denote Spectral Series

Every transition ending in a specific level corresponds to a specific series in the hydrogen spectrum. When the transition ends at the first level, it results in Lyman series, which is in the ultraviolet region of the spectrum. Likewise, transitions ending at the second, third, fourth, and fifth levels correspond to Balmer (visible), Paschen (infrared), Brackett (far infrared), and Pfund (far infrared) series, respectively. Label the spectral series associated with each of the transitions ending in specific levels.

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Most popular questions from this chapter

Which of the following statements is (are) correct for an electron with \(n=4\) and \(m_{\ell}=2 ?\) Explain. (a) The electron is in the fourth principal shell. (b) The electron may be in a \(d\) orbital. (c) The electron may be in a \(p\) orbital. (d) The electron must have \(m_{s}=+\frac{1}{2}\)

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