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Chapter 3: Problem 50

Explain the difference between a ground-state \(\mathrm{H}\) atom and an excited-state H atom.

Short Answer

Expert verified
Answer: The main difference between a ground-state hydrogen atom and an excited-state hydrogen atom is the energy level of their electrons. A ground-state hydrogen atom has its electron in the lowest energy level (n=1), while an excited-state hydrogen atom has an electron in a higher energy level (n>1).

Step by step solution

01

Understanding a Hydrogen Atom

A hydrogen atom consists of one proton in its nucleus and one electron orbiting around it. The energy levels of the electron determine the state of the hydrogen atom.
02

Ground-State Hydrogen Atom

A ground-state hydrogen atom is in the lowest energy state. It means that the electron in the hydrogen atom is present in the lowest energy level (n=1), which is the first orbit around the nucleus, also known as the s orbital or K-shell.
03

Excited-State Hydrogen Atom

An excited-state hydrogen atom has an electron in a higher energy level (n>1) than the ground state. The electron must have absorbed some energy in order to jump from the ground state to an excited state, transitioning to a higher energy orbital around the nucleus. Excited states can have multiple energy levels, such as n=2, n=3, and so on.
04

Comparing Ground-State and Excited-State Hydrogen Atom

The key difference between a ground-state hydrogen atom and an excited-state hydrogen atom is the energy level of their electrons. A ground-state hydrogen atom has its electron in the lowest energy level (n=1), while an excited-state hydrogen atom has an electron in a higher energy level (n>1). Excited state hydrogen atoms are unstable, and will eventually transition back to the ground state by releasing energy in multiple ways (such as emitting light).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ground-State Hydrogen Atom
The ground-state hydrogen atom is the simplest configuration of a hydrogen atom. In this state, the electron occupies the lowest possible energy level or orbit, denoted by \( n=1 \). This is known as the s orbital or K-shell. In this configuration, the electron is closest to the nucleus and has the least potential energy.

Being in the ground state means stability for the hydrogen atom. No external energy is needed to maintain this state. The ground-state serves as the atom's minimal energy configuration, which is why it can persist indefinitely without external influences.
  • Lowest energy level: \( n=1 \).
  • Stable and energetically favored.
  • Electron is closest to the nucleus, minimizing potential energy.
Excited-State Hydrogen Atom
When a hydrogen atom absorbs energy, its electron may jump to a higher energy level, entering what is called an excited state. In an excited-state hydrogen atom, the electron is found in energy levels with \( n > 1 \). These levels are further from the nucleus and have higher energy.

Excited states are temporary because the atom tends to revert to a lower energy configuration. This return to a more stable state often results in the release of energy.
  • Higher energy levels: \( n=2, 3, ... \).
  • Less stable and temporary state.
  • Energy absorption shifts electrons to these higher levels.
Energy Levels in Atoms
In any atom, electrons are organized in specific energy levels or shells around the nucleus. For hydrogen, these energy levels are quantized, meaning the electrons can only occupy certain levels determined by the principal quantum number \( n \).

The levels are arranged from lowest to highest energy. Electrons naturally reside in the lowest available energy level, as this configuration is most stable.
  • Defined by principal quantum number \( n \).
  • Quantized: electrons occupy discrete energy levels.
  • Higher \( n \) means higher energy and greater distance from the nucleus.
Electron Transitions
When electrons in an atom move between energy levels, they undergo what is called electron transitions. These transitions can involve absorbing or emitting energy. If an electron absorbs a specific amount of energy, it can jump from a lower to a higher energy level. Conversely, if it emits energy, it falls to a lower energy level.

These movements are central to understanding phenomena like spectral lines, which are observations of the light emitted or absorbed by electrons moving between levels in an atom.
  • Involves absorption or emission of energy.
  • Results in movement between quantized energy levels.
  • Central to spectral analysis and photon emission or absorption.

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