[Physics Class Notes] on Atomic Spectra Pdf for Exam

The Atomic spectra are defined as the Spectrum of frequencies of electromagnetic radiation emitted or absorbed during transitions of Electrons between Energy levels within an Atom. Each element has a characteristic Spectrum through which it can easily be recognized. In an Atom, Electrons have discrete and some specific energies. There are more Energy states in a tom than there are Electrons. When an Electron transitions from one Energy level to another, it emits light or photon with a specific wavelength. When an Electron gets excited from one Energy level to another, it emits or absorbs light of a specific wavelength.

As an Electron moves between different Energy levels within an Atom, its Spectrum of Electromagnetic radiation is released or absorbed. An Electron emits or absorbs light of a specific wavelength as it jumps from one Energy level to the next.

The Rydberg formula clearly splits the Atomic Hydrogen emission Spectrum into a number of wavelength-dependent spectral lines. The visible spectral lines in the hydrogen emission Spectrum are caused by Atomic transitions between distinct Energy levels. Spectral series are crucial in Astronomical Spectroscopy.

Characteristics of Atomic Spectrum

The characteristics of the Atomic Spectrum are observed as:

1. The Atomic Spectrum should be a pure line Spectrum.

2. The Atomic Spectrum should be the emission band Spectrum. 

3. The Atomic Spectrum should be an absorption line Spectrum.

4. The Atomic Spectrum should be the absorption band Spectrum.

Atomic Spectrum Overview

In any given set of conditions like pressure, temperature, etc., the collection of all these specific wavelengths is what constitutes the Atomic Spectrum. Hence, Atomic spectra are the spectra of Atoms. Below we will be looking at Atomic spectra more in detail along with the Rydberg formula and the spectral series of the hydrogen Atom. There are three types of Atomic spectra: emission spectra, absorption spectra, and continuous spectra.

Spectral Series

Light frequencies emitted by a specific element follow a predictable pattern. For example, because hydrogen is the most basic Atom, it has the most basic Spectrum. At first glance, spectral lines appear to lack order or regularity, but the spacing between lines within certain sets of the hydrogen Spectrum decreases on a regular basis, and each of these sets is known as a spectral series. The first spectral series, known as the Balmer series, was discovered in the visible region of the Hydrogen Spectrum by a Swedish schoolteacher named Johann Jakob Balmer.

H is the red line with the longest wavelength (656.3 nm). The wavelength of the next line in the blue-green Spectrum is 486. 1 nm. The wavelength of the violet Spectrum’s third line is 434.1 nm, and so on.

The Balmer series is as follows in the hydrogen emission Spectrum:

()

As the wavelength decreases, the lines become closer together and less intense.

Rydberg’s Formula

Rydberg’s equation estimates the wavelength of a spectral line in a wide variety of chemical elements in Atomic physics. For all Atomic hydrogen transitions, the equation is a generalisation of the Balmer series.

It is an Energy unit defined in terms of the Electron’s ground-state Energy in the Bohr model of the hydrogen atom. In cgs, “me” is Electron mass, “e” is the Electron charge, h-bar, “Z” is the Atomic number, and “n” is the Electron state’s primary quantum number. The Rydberg formula makes measuring spectral lines simple.

In Atomic physics, Rydberg’s formula calculates the wavelength of a spectral line in many chemical elements. The formula was primarily presented as a generalization of the Balmer series for all Atomic transitions of hydrogen. It is a unit of Energy defined in terms of the ground-state Energy of an Electron in the Bohr model for the hydrogen Atom, in cgs, where is the Electron mass, e is the charge on the Electron, is h-bar, Z is the Atomic number, and n is the principal quantum number for a given Electron state. It becomes easy to calculate the spectral lines by the Rydberg formula. Following is the formula:

[frac{1}{lambda} = RZ^{2} (frac{1}{n’^{2}} – frac{1}{n^{2}})]

R = Rydberg constant (1.09737*107 m-1)

λ = wavelength of light

Z = the Atomic number

n = upper Energy level

n’ = lower Energy level

The spectral series of single-Electron Atoms like hydrogen is Z = 1.

Atomic Spectroscopy

Atomic spectroscopy studies the electromagnetic radiation absorbed or emitted by the Atoms. There are three types of Atomic spectroscopy:

• Atomic Emission Spectroscopy: This includes the transfer of Energy from the ground state to an excited state. The Electronic transition can be discussed in Atomic emission.

• Atomic Absorption Spectroscopy: Absorption to take place, there should be an identical Energy difference between the lower and higher Energy levels. The Atomic absorption spectroscopy principle uses the fact that generating free Electrons in an Atomizer can absorb radiation at specific frequencies. It quantifies the absorption of ground-state Atoms in the gaseous state.

• Atomic Fluorescence Spectroscopy: This is a combination of Atomic emission and Atomic absorption, as it involves radiation of both excitation and de-excitation as well.

Uses of Atomic Spectroscopy

• It is used to identify the spectral lines of materials used in metallurgy.

• It is used in pharmaceutical industries to find the traces of materials used.

• It can be used to study multidimensional elements.

• It is used as a tool for studying the structures of Atoms and molecules.

• It provides a precise analytical method for finding the constituents in a material having unknown chemical composition.

• Atomic spectroscopy is used in occupational and environmental monitoring. 

Solved Examples

Question: An Electron excites an Atom to the fourth orbit, so when it jumps back to the Energy levels, a Spectrum is formed. A total number of spectra is formed. What would be the total number of spectral lines in this Spectrum?

Answer: An Electron excites in an Atom to the fourth orbit, n=4.

The total number of spectral lines in the Spectrum is,

[frac{n(n – 1)}{2} = frac{4(4 – 1)}{2} = frac{4times 3}{2} = 6
]

Fun Facts

When Atoms get excited, they emit certain specific wavelengths that correspond to different colors. The emitted light can be noted as a series of colored lines with dark spaces in between, this colored lines series is called a line of Atomic spectra. A unique set of spectral lines is produced through each element. Rainbow is an example of a continuous Spectrum.