18 Questions
What can be inferred from the fact that the coefficients for absorption and stimulated emission are numerically equal?
The probability of an upward transition is equal to that of a downward transition.
What is the relation between the ratio of coefficients of spontaneous versus stimulated emission and the frequency of radiation?
It is proportional to the third power of the frequency.
What is required for light amplification to occur?
Stimulated emission should occur almost exclusively.
What can be said about the lifetime of the upper state in relation to light amplification?
It is very short.
What type of light is produced when radiating atoms are incoherent?
Incoherent light.
What is the name given to equations (24.14) and (24.15) that relate the Einstein coefficients?
The Einstein relations.
Which Einstein coefficient represents spontaneous emission?
A21
In what condition are B12 and B21 equal?
When the energy levels E1 and E2 are nondegenerate
Which Einstein coefficient is related to the transition from the higher energy level E2 to the lower energy level E1?
B21
What happens when spontaneous emission occurs from an atom?
Atom emits a photon and loses energy
When does the spontaneous transition coefficient A21 become non-zero?
When the atom is in an excited state
What is the relationship between spontaneous emission and the lifetime of the excited state?
Shorter lifetime of the excited state implies quicker spontaneous emission
What is the probability that a spontaneous transition occurs given by?
(P2)SpontaneousA1
What does the radiative rate, A,, measure?
The lifetime of the upper state against spontaneous decay
What is the constant of proportionality known as the Einstein coefficient for stimulated emission?
B,,
What is the lifetime of the upper state against spontaneous decay to the lower state related to?
The radiative rate
What is the probability that an absorption transition occurs given by?
P2 = Bp(v)
What is the likelihood of a radiant atom at the excited state spontaneously jumping to a lower level?
Higher than the likelihood of being stimulated by a photon
Study Notes
Planck's Law and Einstein Relations
- Planck's law is defined as p(v) = 1 / (u(v)/c), where u is the refractive index of the medium and c is the velocity of light in free space.
- The energy density p(v) is given by cqu (24.12), which is consistent with Planck's law (24.13) only if &rhv'u A1 and B2 = | or B2B1 (Einstein relations).
- The Einstein relations (24.14) and (24.15) show that the coefficients for absorption and stimulated emission are numerically equal.
Einstein Coefficients
- There are three Einstein coefficients: A, B, and B.
- A1 is the coefficient for spontaneous emission, which is a constant characteristic of the atom and represents the properties of the energy states E, and E.
- B1 is the coefficient for induced absorption, which is a constant characteristic of the atom and represents the properties of the energy states E, and E.
- B2 is the coefficient for stimulated emission, which is equal to B1 under the special condition that the quantum states E, and E, are single energy levels (non-degenerate levels).
Relations between Einstein Coefficients
- The Einstein coefficients A, B, and B, are interconnected.
- The relation between the coefficients is derived assuming that the atoms and the radiation are in thermal equilibrium and the radiation is identical with black body radiation.
- The coefficients are related through B2 = | or B2B1, and A,1 = 0, since spontaneous transition cannot take place from lower energy state E, to higher energy state E.
Light Amplification
- Light amplification requires that stimulated emission occur almost exclusively.
- The probability of an upward (absorption) transition is equal to the probability of a downward (stimulated) transition.
- The ratio of coefficients of spontaneous versus stimulated emission is proportional to the third power of the frequency of the radiation, making it difficult to achieve laser action in higher frequency ranges such as X-rays.
Learn about the Einstein coefficients that are related to induced transitions in atoms, such as transitions induced by external photons. Explore how B,, represents transitions from lower to higher energy levels, and B,, denotes transitions from higher to lower energy levels.
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