How can we get the total number of electrons, Physics

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How can we get the total number of electrons

Assignment task: Let say we need to get the total number of electrons of an atom (for example, a sphere shape silicon atom) using numerical/mathematical approach.

Q1. How can we get the total number of electrons using 'spherical integration' of density of states?

Q2. How can we get the total number of electrons using 'spherical integration' of partial density of states?

Please show relevant spherical integration equations and their meanings, and necessary diagram if any.

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Physics: How can we get the total number of electrons

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