What Are B and A Coefficients in Emission Processes?

TL;DR

The B and A coefficients in emission processes represent the rates of stimulated and spontaneous emissions, respectively. They are found to be equal, which simplifies calculating transition rates. At low temperatures, spontaneous emission dominates due to fewer photons, while at higher temperatures, stimulated emission prevails as photon density increases.

Transcript

PROFESSOR: OK, so that's our equation. Three terms-- first term, spontaneous emission, second term, stimulated emission proportional to Nb, third term increases Nb's absorption. Our strategy now is, so what do you do with this? This looks like a good equation, but what are we to do? We haven't used three, really. So we can solve for U. And this tim... Read More

Key Insights

• ☠️ The equation for the rates of spontaneous and stimulated emission can be manipulated to solve for the value of U.
• 🟰 The coefficients for spontaneous and stimulated emission are found to be equal.
• 😃 Calculating the B coefficients allows for the determination of the A coefficient.
• 🤔 Spontaneous emission can be thought of as being stimulated by vacuum fluctuations of the electromagnetic field.

Questions & Answers

Q: What are the three terms in the equation for the rates of spontaneous and stimulated emission?

The three terms represent spontaneous emission, stimulated emission proportional to the number of photons, and absorption due to the number of photons.

Q: How is U solved for in the equation?

U is solved for by dividing the equation by Nb and rearranging the terms to group the U term on one side.

Q: What is the significance of the discovery that the coefficients for spontaneous and stimulated emission are equal?

This discovery simplifies the calculation of transition rates, as calculating the B coefficients allows for the determination of the A coefficient.

Q: How do spontaneous and stimulated emission differ in terms of their contribution to atomic transitions?

At low temperatures, spontaneous emission dominates as there are fewer photons available, while at high temperatures, stimulated emission dominates due to the increased number of photons.

Summary & Key Takeaways

• The equation for the rates of spontaneous and stimulated emission is derived, with three terms representing spontaneous emission, stimulated emission proportional to the number of photons, and absorption due to the number of photons.

• The goal is to solve for U, which can be done by dividing the equation by Nb and rearranging the terms.

• Comparisons are made with the thermal radiation formula, leading to the discovery that the coefficients for spontaneous and stimulated emission are equal, simplifying the calculation of transition rates.