Question

What is the Saha equation?

Answer 1

To solve the given question in which we have to tell what is Saha’s equation we will first discuss about where we use Saha’s equation in physics and then we will discuss what does Saha’s equation tells us after which we will write the Saha’s equation and also what does all the symbols mean.

Complete step by step answer:
Saha’s equation is a very useful result that combines the quantum mechanics and the statistical mechanics together so with the help of this equation we can explain the spectral classification of the stars.
Saha’s equation tells us about the degree of ionization of any gas in thermal equilibrium by relating it to the pressure and temperature of the gases. The Saha’s equation also depicts the dependence of ionization of the gases on various physical parameters. The Saha equation is somewhat related to the state of ionization of the gases in thermal equilibrium to the temperature and pressure of the gases.
Now, let us consider the mathematical form of Saha’s equation. Saha’s equation, when considered mathematically, may be a relationship that is acting between the observed spectra of stars and their temperatures and pressures. This equation was first time stated in 1920 by the Indian astrophysicist Meghnad N. Saha. It helps us to understand how the ionization state of any particular element in a star changes with varying temperatures and pressures. The spectrum of stars is directly related to the relative numbers of atoms and ions they contain because each atom or ion can absorb or emit radiation of a particular set of wavelengths.
Now, let us write the Saha’s equation:

& \dfrac{kT}{h} \\\ & 2 \\\ \end{aligned}}{{e}^{-[{{E}_{i+1}}-{{E}_{i}}]/kT}}$$ where, $${{N}_{i+1}}$$and $${{N}_{i}}$$are the number of atoms in the $$(i+1)^{th}$$ and $$(i)^{th}$$ ionization states, respectively; $${{U}_{i+1}}$$ and $${{U}_{i}}$$describes how energy is partitioned among the $$(i+1)^{th}$$ and $$(i)^{th}$$states; $${{E}_{i+1}}$$and $${{E}_{i}}$$are the energies of the ionization states; $${{N}_{e}}$$is the number of electron; and $$T$$is the temperature. The other quantities in the given equation are physical constants where $${{m}_{e}}$$is the mass of electrons $$K$$is the Boltzmann constant and h is the planck's constant. **Note:** Saha gave a mathematical formula that describes how the excitation and ionization in the stellar atmospheres are actually dependent on the conditions of temperature and pressure prevailing in those stars and not just the composition. Saha’s equation actually laid the foundation of a very important branch of Astrophysics known as – Stellar Spectroscopy.