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Titration Calculations: Strong Acid - Strong Base02:28

Titration Calculations: Strong Acid - Strong Base

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Calculating pH for Titration Solutions: Strong Acid/Strong Base
A titration is carried out for 25.00 mL of 0.100 M HCl (strong acid) with 0.100 M of a strong base NaOH. The pH at different volumes of added base solution can be calculated as follows:
(a) Titrant volume = 0 mL. The solution pH is due to the acid ionization of HCl. Because this is a strong acid, the ionization is complete and the hydronium ion molarity is 0.100 M. The pH of the solution is then:
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Atomic Structure01:33

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Acids, Bases and Neutralization Reactions03:26

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An acid-base reaction is one in which a hydrogen ion, H+, is transferred from one chemical species to another. Such reactions are of central importance to numerous natural and technological processes, ranging from the chemical transformations within cells or lakes and oceans to the industrial-scale production of fertilizers, pharmaceuticals, and other substances essential to the society.
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Strong Acid and Base Solutions03:22

Strong Acid and Base Solutions

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A strong acid is a compound that dissociates completely in an aqueous solution and produces a concentration of hydronium ions equal to the initial concentration of acid. For example, 0.20 M hydrobromic acid will dissociate completely in water and produces 0.20 M of hydronium ions and 0.20 M of bromide ions.
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Titration of a Strong Acid with a Strong Base01:23

Titration of a Strong Acid with a Strong Base

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During the titration of a strong acid with a strong base, pH calculations are primarily based on the concentration of residual hydronium or hydroxide ions. Initially, a strong acid like hydrochloric acid fully dissociates, creating hydronium and chloride ions, resulting in a low pH. The addition of a strong base like sodium hydroxide alters the concentration of hydronium ions by neutralizing them. As more base is added, the pH gradually increases. At the equivalence point, all hydronium ions...
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Social Traps

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Social traps are negative situations where people get caught in a direction or relationship that later proves to be unpleasant, with no easy way to back out of or avoid. The concept was orignally introduced by John Platt who applied psychology to Garrett Hardin's "Tragedy of the Commons", where in New England herd owners could let their cattle graze in the common ground. This situation seems like a good idea, but an individual could have an advantage. If they owned...
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Construction and Characterization of External Cavity Diode Lasers for Atomic Physics
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Strong Purcell Effect on a Neutral Atom Trapped in an Open Fiber Cavity.

J Gallego1, W Alt1, T Macha1

  • 1Institut für Angewandte Physik der Universität Bonn, Wegelerstrasse 8, D-53115 Bonn, Germany.

Physical Review Letters
|November 10, 2018
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Summary

Researchers observed a sixfold Purcell broadening in a trapped Rubidium-87 atom coupled to a fiber cavity. This significant enhancement directs most atomic fluorescence into the cavity, enabling efficient fiber-coupled photonic interfaces.

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Area of Science:

  • Atomic Physics
  • Quantum Optics
  • Cavity Quantum Electrodynamics (cQED)

Background:

  • Optically trapped neutral atoms are crucial for quantum information processing.
  • Strong coupling between atoms and optical cavities enhances light-matter interactions.
  • Fiber cavities offer robust and efficient interfaces for quantum technologies.

Purpose of the Study:

  • To investigate the Purcell enhancement of an atom coupled to a fiber cavity.
  • To quantify the efficiency of fluorescence emission into the cavity mode.
  • To explore the potential of this system for photonic interfaces.

Main Methods:

  • Utilizing an optically trapped Rubidium-87 atom.
  • Strongly coupling the atom to a high-finesse fiber cavity.
  • Measuring atomic fluorescence and photon statistics under laser illumination.
  • Analyzing the photon autocorrelation function to confirm sub-Poissonian statistics and Purcell enhancement.

Main Results:

  • Observed a sixfold Purcell broadening of the Rubidium-87 D2 line.
  • Demonstrated up to 90% of atomic fluorescence coupled into the cavity mode.
  • Confirmed sub-Poissonian statistics of cavity output and enhanced atomic decay rate.
  • Identified photon leakage as the dominant field decay channel (κ≈2π×50 MHz).

Conclusions:

  • Strong atom-fiber cavity coupling enables efficient channeling of atomic fluorescence.
  • The observed Purcell enhancement and sub-Poissonian statistics are key indicators of high-quality light-matter interaction.
  • This system provides a high-bandwidth, fiber-coupled platform for quantum memories and single-photon sources.