It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

The chemical and physical properties of plasma membranes cause them to be selectively permeable. Since plasma membranes have both hydrophobic and hydrophilic regions, substances need to be able to transverse both regions. The hydrophobic area of membranes repels substances such as charged ions. Therefore, such substances need special membrane proteins to cross a membrane successfully. In  facilitated transport, also known as facilitated diffusion, molecules and ions travel across a...

In contrast to passive transport, active transport involves a substance being moved through membranes in a direction against its concentration or electrochemical gradient. There are two types of active transport: primary active transport and secondary active transport. Primary active transport utilizes chemical energy from ATP to drive protein pumps that are embedded in the cell membrane. With energy from ATP, the pumps transport ions against their electrochemical gradients—a direction...

One example of how cells use the energy contained in electrochemical gradients is demonstrated by glucose transport into cells. The ion vital to this process is sodium (Na+), which is typically present in higher concentrations extracellularly than in the cytosol. Such a concentration difference is due, in part, to the action of an enzyme “pump” embedded in the cellular membrane that actively expels Na+ from a cell. Importantly, as this pump contributes to the high concentration of...

In eukaryotes, transcription and translation are compartmentalized; an mRNA is first synthesized in the nucleus and then selectively transported to the cytoplasm for protein synthesis. Before transport, a pre-mRNA undergoes several steps of post-transcriptional modifications including splicing, 5' capping, and the addition of a poly-adenine tail. Various proteins bind to the pre-mRNA during these modifications. The mRNA transport takes place with the help of multiple proteins playing...