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Conjugated dienes have lower heats of hydrogenation than cumulated and isolated dienes, making them more stable. The enhanced stabilization of conjugated systems can be understood from their π molecular orbitals.
The simplest conjugated diene is 1,3-butadiene: a four-carbon system where each carbon is sp2-hybridized and has an unhybridized p orbital that contains an unpaired electron. According to molecular orbital theory, atomic orbitals combine to form molecular orbitals such that the number...

Life on Earth is carbon-based, as all macromolecules that make up living organisms contain carbon atoms. All organic compounds have a carbon backbone. Each carbon atom is tetravalent and can bond with four other atoms, making it an extraordinarily flexible component of biological molecules. Because carbon’s valence electrons are stable, it rarely becomes an ion. As the carbon chain increases in length, structural modifications such as ring structures, double bonds, and branching side chains...

The motion of a rocket is governed by the conservation of momentum principle. A rocket's momentum changes by the same amount (with the opposite sign) as the ejected gases. As time goes by, the rocket's mass (which includes the mass of the remaining fuel) continuously decreases, and its velocity increases. Therefore, the principle of conservation of momentum is used to explain the dynamics of a rocket's motion. The ideal rocket equation gives the change in velocity that a rocket experiences by...

The driving force for the motion of any vehicle is friction, but in the case of rocket propulsion in space, the friction force is not present. The motion of a rocket changes its velocity (and hence its momentum) by ejecting burned fuel gases, thus causing it to accelerate in the direction opposite to the velocity of the ejected fuel. In this situation, the mass and velocity of the rocket constantly change along with the total mass of ejected gases. Due to conservation of momentum, the rocket's...

Allyl radicals are three-carbon conjugated systems. They are readily formed as intermediates in halogenation reactions of alkenes involving the addition of halogen to the allylic carbon instead of the double bond. As seen in allyl cations and anions, each of the three sp2-hybridized carbon atoms in allyl radicals has an unhybridized p orbital. These orbitals combine to give three π molecular orbitals.
The allyl systems have identical molecular orbitals but differ in the number of π electrons.

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.