Pi Electron Count

Pi electron count is the number of electrons occupying the delocalized pi molecular orbitals of a conjugated system, a key concept for understanding bonding, aromaticity, and molecular stability. In a continuous array of aligned p orbitals, each pi bond typically contributes two electrons, while lone pairs, carbocations, or negative charges contribute according to their orbital participation; cyclic systems can then be evaluated using Hückel’s 4n + 2 rule. Counting pi electrons helps classify rings as aromatic, antiaromatic, or nonaromatic and supports predictions of resonance stabilization, molecular geometry, and chemical reactivity.

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Education

JoVE Core - Civil Engineering

The Buckingham Pi Theorem

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2025

The Buckingham Pi theorem provides a structured method to simplify fluid dynamics problems by reducing complex systems of variables to dimensionless terms. In analyzing flow through a pipe, variables that define the system include the pipe's diameter, the fluid's velocity, its density, and viscosity. These can be combined into a single dimensionless term, the Reynolds number (Re), which captures their essential relationship. The first step in applying the Buckingham Pi theorem is identifying...

Determination of Pi Terms

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2025

The Buckingham Pi theorem is a valuable method in dimensional analysis, reducing complex relationships between variables into dimensionless terms. Relevant variables in analyzing the lift force on an airplane wing include lift force, air density, wing area, aircraft velocity, and air viscosity. Expressing each variable in terms of fundamental dimensions — mass, length, and time — provides a consistent foundation for constructing these dimensionless terms. The theorem indicates that the number...

PI Controller: Design

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2024

Proportional Integral (PI) controllers are a fundamental component in modern control systems, widely used to enhance performance and mitigate steady-state errors. They are particularly effective in applications such as automatic brightness adjustment on smartphones, where they excel at mitigating steady-state errors for step-function inputs. Unlike PD controllers, which require time-varying errors to function optimally, PI controllers leverage their integral component to address residual...

Using a Hemacytometer to Count Cells

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2023

Many biomedical experiments require manipulation of a known quantity of cells, in order to achieve accurate, reproducible, and statistically-relevant data. Therefore, learning how to count cells is a particularly essential technique for any successful biomedical scientist. The most common way to count cells is by using a hemacytometer - an instrument that bears two laser-etched grids, which aid in the enumeration of an aliquot cells under a simple light microscope. This data can then be used to...

Research

JoVE Journal - Biology

Counting and Determining the Viability of Cultured Cells

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Cited by 19 •

2008

Determining the number of cells in culture is important in standardization of culture conditions and in performing accurate quantitation experiments. In this video, we demonstrate how cells are counted using a hemacytometer.

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