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Quantum Numbers

Quantum Numbers

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.

The Quantum-Mechanical Model of an Atom

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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.

Conjugated Proteins

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Conjugated Proteins

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The Dot Product

The Dot Product

Measuring how one directional quantity affects another along a specific path involves comparing their orientation and strength. When two such quantities are represented using direction and amount, a numerical result is computed to show how much one acts along the path of the other. This result comes from a rule combining both inputs' horizontal and vertical parts and adding the results.This calculation gives a single value that grows larger when both inputs point in similar directions and...

Dot Product

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The dot product is an essential concept in mathematics and physics.
In engineering, the dot product of any two vectors is the product of the magnitudes of the vectors and the cosine of the angle between them. It is denoted by a dot symbol between the two vectors.
Consider a vehicle pulling an object along the ground using a rope. If the rope makes an angle with the horizontal axis, the work done can be calculated using the dot product of the force applied and the object's displacement.
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Related Experiment Video

Updated: Feb 9, 2026

Compact Quantum Dots for Single-molecule Imaging

Compact Quantum Dots for Single-molecule Imaging

Published on: October 9, 2012

Quantum Dot-Dye Conjugates for Biosensing, Imaging, and Therapy.

Sungwook Jung¹, Xiaoyuan Chen¹

¹Laboratory of Molecular Imaging and Nanomedicine, National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health, Bethesda, MD, 20892, USA.

Advanced Healthcare Materials

|June 5, 2018

Summary

Quantum dot-dye conjugates offer advanced biosensing and imaging by harnessing Förster resonance energy transfer (FRET) and electron transfer (eT). These systems enable sensitive detection of biomolecules and improved photodynamic cancer therapy.

Keywords:

Förster resonance energy transfer (FRET)biosensing molecular imaging photodynamic therapy (PDT)quantum dots

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Last Updated: Feb 9, 2026

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Published on: July 11, 2012

Area of Science:

Nanotechnology
Biochemistry
Materials Science

Background:

Quantum dots (QDs) possess unique optical properties.
Conjugating dyes to QDs enables Förster resonance energy transfer (FRET) and electron transfer (eT).
These interactions modify fluorescence and trigger photochemical reactions like singlet oxygen generation.

Purpose of the Study:

To review recent advances in QD-dye conjugates.
To highlight applications in biosensing, bioimaging, and photodynamic therapy.
To summarize systems utilizing FRET or eT for fluorescence readout or photochemical reactions.

Main Methods:

Conjugation of dyes onto the surface of quantum dots.
Utilizing FRET and eT mechanisms for signal transduction.
Developing photoactivatable and photoswitchable probes for imaging.

Main Results:

QD-dye conjugates function as sensitive biosensors for various analytes (pH, O2, ions, miRNA, etc.).
These conjugates are effective for fluorescence super-resolution imaging.
QD-dye systems facilitate repetitive singlet oxygen generation for cancer treatment and deep tissue imaging.

Conclusions:

QD-dye conjugates represent a versatile platform for advanced biosensing and bioimaging.
They offer significant potential in photodynamic cancer therapy and deep tissue imaging.
The controlled FRET and eT processes are key to their diverse functionalities.