One of the most fundamental and fascinating concepts in atomic physics is the emission of monochromatic radiation when an electron in a hydrogen atom moves between energy levels. This process explains how light is emitted and why we observe distinct spectral lines in hydrogen’s emission spectrum.
The Bohr model of the hydrogen atom provides a simple yet powerful explanation of this phenomenon. When an electron transitions from a higher energy level to a lower one, it emits a photon of specific energy and wavelength, creating monochromatic radiation.
This topic explores the concept of monochromatic radiation, energy levels of hydrogen, spectral series, and real-world applications of this phenomenon.
Understanding Monochromatic Radiation
What is Monochromatic Radiation?
Monochromatic radiation refers to electromagnetic radiation (light) consisting of a single wavelength or frequency. The word "monochromatic" comes from the Greek words mono (single) and chroma (color), meaning "single-colored light."
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A laser beam is an example of monochromatic radiation.
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A hydrogen atom emits monochromatic radiation when its electron transitions between energy levels.
Why is Hydrogen Important in Atomic Physics?
Hydrogen is the simplest atom, consisting of:
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One proton (nucleus)
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One electron orbiting around the nucleus
Despite its simplicity, hydrogen plays a crucial role in quantum mechanics and spectroscopy.
Energy Levels of Hydrogen and Electron Transitions
Quantized Energy Levels
According to Niels Bohr’s atomic model, the electron in a hydrogen atom exists in discrete energy levels (quantized orbits). These levels are given by:
Where:
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** E_n ** is the energy of the electron in the n-th orbit
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** n ** is the principal quantum number (1, 2, 3, …)
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13.6 eV is the ionization energy of hydrogen
The higher the energy level, the less negative the energy value.
Electron Transition and Photon Emission
When an electron moves from a higher energy level to a lower one, the energy difference is released as a photon of light. The energy of this photon is given by:
Using Planck’s equation, the wavelength of the emitted photon is:
Where:
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** h = 6.626 à 10â»Â³â´ J·s** (Planck’s constant)
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** c = 3.00 à 10⸠m/s** (speed of light)
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** E_{text{photon}} ** is the energy released
This emitted photon is monochromatic, meaning it has a specific wavelength and frequency.
Spectral Series of Hydrogen
Hydrogen’s emission spectrum consists of several spectral series, each corresponding to electron transitions to a particular lower energy level.
1. Lyman Series (Ultraviolet Region)
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**Electron transitions to n = 1 **
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Produces ultraviolet (UV) radiation
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Example: **Transition from n = 2 to n = 1 ** emits a 121.6 nm photon
2. Balmer Series (Visible Light Region)
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**Electron transitions to n = 2 **
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Produces visible light
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Example: **Transition from n = 3 to n = 2 ** emits a 656.3 nm red light
3. Paschen Series (Infrared Region)
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**Electron transitions to n = 3 **
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Produces infrared radiation
4. Brackett, Pfund, and Humphreys Series (Infrared & Microwaves)
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**Electron transitions to n = 4, 5, 6 **
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Emit infrared and microwave radiation
Monochromatic Radiation in Hydrogen: Key Examples
Case 1: Electron Falls from n = 3 to n = 2 (H-alpha Line, Balmer Series)
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Initial energy level: n = 3
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Final energy level: n = 2
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Energy difference: $1.89$ eV
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Wavelength: $656.3$ nm (red light)
This transition creates the H-alpha spectral line, commonly seen in astronomy.
Case 2: Electron Falls from n = 2 to n = 1 (Lyman Series, UV Radiation)
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Initial energy level: n = 2
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Final energy level: n = 1
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Energy difference: $10.2$ eV
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Wavelength: $121.6$ nm (ultraviolet light)
This transition is important in ultraviolet spectroscopy.
Applications of Hydrogen’s Monochromatic Radiation
1. Spectroscopy and Astrophysics
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Helps scientists identify elements in stars and galaxies.
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Used to study the composition of interstellar matter.
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The redshift of hydrogen lines helps measure the expansion of the universe.
2. Quantum Mechanics and Atomic Physics
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The hydrogen spectrum was critical in the development of quantum theory.
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Used in educational demonstrations of atomic structure.
3. Medical and Technological Applications
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Hydrogen discharge lamps are used in scientific instruments.
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Ultraviolet hydrogen lamps are used for sterilization.
4. Lasers and Optical Devices
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Hydrogen’s monochromatic spectral lines are used in calibration of optical instruments.
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Essential in the design of high-precision spectrometers.
Why is Hydrogen’s Radiation Monochromatic?
1. Discrete Energy Levels
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Hydrogen electrons can only occupy specific energy levels.
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When they transition, they emit a single, specific photon.
2. Conservation of Energy
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The emitted photon’s energy exactly matches the energy gap between levels.
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This results in pure, monochromatic light.
3. No Intermediate Transitions
- Electrons jump directly between levels, ensuring a fixed wavelength.
Key Takeaways
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Hydrogen emits monochromatic radiation when its electron transitions between energy levels.
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The wavelength of emitted light depends on the energy difference between initial and final states.
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The hydrogen spectrum is divided into series:
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Lyman (UV)
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Balmer (Visible)
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Paschen, Brackett, Pfund (Infrared)
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The emitted radiation has many applications in astronomy, spectroscopy, quantum mechanics, and technology.
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Hydrogen’s spectral lines are crucial in understanding atomic structure and the quantum behavior of electrons.
The emission of monochromatic radiation from hydrogen atoms is one of the most significant discoveries in atomic physics. By studying electron transitions and spectral lines, scientists have unlocked crucial insights into quantum mechanics, astronomy, and spectroscopy.
From understanding the composition of stars to designing advanced optical instruments, the monochromatic radiation emitted by hydrogen plays an essential role in both theoretical and practical applications.