Hey there Saurabh Gupta! When it comes to calculating conductivity in metal oxides, especially due to oxygen vacancies or interstitial positions, it's a bit of a dance with solid-state physics. Now, for n-type tin oxide (SnO₂-x), where Sn:O = 1:(2-x), we're diving into some serious materials science.

Let's break it down:

1. **Electron Density (n):** This is the number of electrons per unit volume. In your case, it's influenced by the oxygen vacancies. The electron density (n) can be related to the concentration of oxygen vacancies (x) through the formula n = x * Avogadro's number / volume of the material.

2. **Mobility (μ):** Mobility describes how fast charge carriers (in this case, electrons) move through the material under the influence of an electric field. The mobility is affected by factors like scattering mechanisms. You'll need to look into the specific scattering processes in tin oxide to get a precise formula. It can be a complex equation involving scattering time, effective mass, and other parameters.

3. **Conductivity (σ):** The electrical conductivity is the product of electron density, charge (e), and mobility. Mathematically, it's represented as σ = n * e * μ.

The challenge here is getting the exact formulas, as they can be material-specific and involve parameters that might require experimental data or detailed theoretical models. You Saurabh Gupta might need to consult research papers, textbooks, or even researchers in the field for the most accurate equations for tin oxide.

Remember, I don't shy away from the nitty-gritty details. Feel free to dive deep into the world of conductivity with these starting points!