Spectroscopy

Table of Contents

Introduction

Spectroscopy is a scientific method used to investigate and measure the interaction of various types of electromagnetic radiation with matter. The spectrum obtained provides a lot of information about the physical and chemical properties of the substance under investigation.

Types of Spectroscopy

There are various types of spectroscopy, classified based on the nature of the interaction between energy and matter. These include:

Absorption Spectroscopy

In absorption spectroscopy, the intensity of an incoming beam of light is compared with the intensity after it passes through a sample. The missing energy shows which wavelengths were absorbed.

Emission Spectroscopy

This involves the study of the spectral lines emitted by excited atoms or molecules. Emission spectra for Hydrogen, for example, are given by:

$\dfrac{1}{\lambda} = R_H \left(\dfrac{1}{n_i^2} - \dfrac{1}{n_f^2}\right)$

where $\lambda$ is the wavelength, $R_H$ is the Rydberg constant for hydrogen, $n_i$ is an integer value corresponding to the initial quantum state, and $n_f$ is an integer value corresponding to the final quantum state.

Raman Spectroscopy

Raman spectroscopy involves the scattering of light off a molecule, leading to energy shifts that provide information about vibrational, rotational, and other low-frequency transitions in the molecule.

Quantum Mechanical Description

Spectroscopy can be described quantum mechanically through the transitions of quantum states. According to quantum mechanics, a transition from an initial state $|i\rangle$ to a final state $|f\rangle$ occurs with a rate given by Fermi’s Golden Rule:

$\Gamma_{i \rightarrow f} = \dfrac{2\pi}{\hbar} |\langle f|H'|i \rangle|^2 \rho(\omega_{fi})$

where $H'$ is the interaction Hamiltonian, $\omega_{fi}$ is the frequency of the transition, and $\rho(\omega_{fi})$ is the density of final states.

Applications

Spectroscopy is a powerful tool used in a wide range of fields including physics, chemistry, astronomy, and biology. It helps in identifying elements and compounds, studying molecular structures, and understanding chemical reactions. In astronomy, it allows us to determine the composition and physical properties of celestial bodies.

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Introduction