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What is the total number of electrons that can be held in all orbitals having the same principal quantum number $n ?$

The maximum number of electrons than can share the same shell, or principa quantum number $(\mathrm{n}),$ can be calculated as follows $\mathrm{N}$ of electrons $=2 \cdot n^{2}$ Therefore, in the first shell $(\boldsymbol{n}=1)$ there can be $2 \cdot 1^{2}=2 \cdot 1=2$ electronsIn the second shell $(\boldsymbol{n}=2)$ $2 \cdot 2^{2}=2 \cdot 4=8$ electrons.In the third shell $(\boldsymbol{n}=3)$ $2 \cdot 3^{2}=2 \cdot 9=18$ electrons

Chemistry 101

Chapter 7

Quantum Theory and the Electronic Structure of Atoms

Electronic Structure

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04:49

In chemistry and physics, electronic structure is the way the electrons of an atom are arranged in relationship to the nucleus. It is determined by the subshells the electrons are bound to, which are in turn determined by the principal quantum number ("n") and azimuthal quantum number ("l"). The electrons within an atom are attracted to the protons in the nucleus of that atom. The number of electrons bound to the nucleus is equal to the number of protons in the nucleus, which is called the atomic number ("Z"). The electrons are attracted to the nucleus by this mutual attraction and are bound to the nucleus. The electrons within an atom are attracted to each other and this attraction determines the electron configuration. The electron configuration is described by the term symbol, which is the letter used to identify each subshell.

16:45

In physics, the wave–particle duality is the concept that every object or process, no matter how large or how small, behaves as both a wave and a particle. The wave–particle duality is one of the central concepts in quantum mechanics.

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Okay. The standard rule for finding out how many electrons can be held in each principal quantum number is the equation. Uh, well, say electron total is equal to to times and square where n is the principal quantum number. So if we have, let's say, for example, three p. We're talking about this orbital right here. If you might know off, stop your head that a P orbital can hold by itself. Six electrons. Okay, But when we talk about total, we need to think about all of the shapes and all the horribles included in this built up to this. So this would be one s two s to p three s, so we would say to times three squared is nine. So we we get 18 total electrons in this orbital and all of the orbital's adding up to that. All right, so another example would say six d. All right, so this would be to time six squared to six square we know is 36 that times two would equal 72 electrons. So this 60 this is a really big Adam. This would be think, somewhere in the transition elements, possibly in the radioactive area. So this is your general rule of thumb when you're trying to find the total number of electrons

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