Written by Dr. Charudatta Pathak• August 3, 2024• 9:49 pm• Atomic Physics

Atomic Spectrum of Hydrogen: Absorption and Emission Spectra

HomeAtomic PhysicsAtomic Spectrum of Hydrogen: Absorption and Emission Spectra

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In this article we will explore atomic spectrum of hydrogen. I will focus on continuous and line spectra, Balmer and Lyman series. I will explain this topic using solved numerical problems to deepen your understanding of quantum mechanics.

Keywords

Atomic spectrum of hydrogen, absorption spectrum, emission spectrum, continuous spectrum, line spectrum, Bohr model, quantum mechanics, Lyman series, Balmer series, Rydberg constant, spectroscopy, hydrogen spectrum series, wavelength calculation.

Table of Contents

Introduction to Spectra

When we talk about spectrum, we refer to the group of radiations or wavelengths obtained when light splits. Consider sunlight; when passed through a prism, it bends at different angles to display 7 distinct colors. These colors represent different radiations or wavelengths, collectively known as the spectrum.

Types of Spectrum

Continuous Spectrum

A continuous spectrum is similar to what we see in a rainbow. Three critical points to remember about continuous spectra:

No clear boundary between colors.
Colors partially overlap.
No separating lines between colors.

Line Spectrum

In contrast, a line spectrum (or discontinuous spectrum) is observed in a fluorescent lamp. Key points about line spectra:

Clear boundary lines between colors.
No overlapping of colors.
Distinct separation between colors.

Absorption and Emission Spectra

There are two types of line spectra: absorption spectrum and emission spectrum.

Absorption Spectrum: When white light passes through an atom, the atom absorbs specific wavelengths. This results in missing wavelengths in the spectrum.
Emission Spectrum: After absorbing energy, the atom eventually emits wavelengths which can be observed as distinct lines on a dark background.

Atomic Spectrum of Hydrogen

Bohr Model Explanation

Consider a hydrogen atom in its ground state. When energy is provided, an electron absorbs this energy and jumps to a higher energy level. This excited electron then loses its energy in the form of radiation, equal to the energy difference between the levels, $\Delta E = E2 - E1$

Numerical Example

To find the energy emitted when an electron from a hydrogen atom transitions from the ( n=2 ) to ( n=1 ) energy level, you can use Bohr’s formula:

$\Delta E = 13.6 \left( \frac{1}{n1^2} - \frac{1}{n2^2} \right) \ = 13.6 \left( 1 - \frac{1}{4} \right) = 10.2 \text{eV}$

Calculating Wavelength of Emitted Radiation

Using the relationship $E = \frac{hc}{\lambda}$

$\frac{1}{\lambda} = R \left( \frac{1}{n1^2} - \frac{1}{n2^2} \right)$

Where ( R ) is the Rydberg constant, it is possible to calculate the wavelength.

Hydrogen Atomic Spectrum Series

Lyman Series

Transition: Electrons jump to ( n=1 ).
Region: Ultraviolet.
Shortest Wavelength: 911 Å.
Longest Wavelength: 1216 Å.

Balmer Series

Transition: Electrons jump to ( n=2 ).
Region: Visible.
Longest Wavelength: 6559.2 Å.

Baschen Series

Transition: Electrons jump to ( n=3 ).
Region: Near Infrared.
Shortest Wavelength: 8199 Å.

Brackett Series

Transition: Electrons jump to ( n=4 ).
Region: Mid Infrared.

Pfund Series

Transition: Electrons jump to ( n=5 ).
Region: Far Infrared.

Conclusion

Understanding the atomic spectrum of hydrogen is crucial for delving into the complexities of quantum mechanics and spectroscopy. Whether it’s the continuous or line spectra, absorption or emission spectra, the detailed calculations, and series names, each aspect builds a comprehensive knowledge base essential for further study.

Feel free to leave comments or questions below, and don’t forget to share this post with your friends and colleagues interested in physics and quantum mechanics!