How do you derive Einstein's relation for diffusion and difference between stimulated absorption and stimulated emission?
Tehmina Khan
Stimulated Absorption:Definition: Occurs when an atom or molecule absorbs a photon and transitions from a lower energy state to a higher one due to the influence of an external electromagnetic field. Process: The incoming photon stimulates the atom to absorb its energy and move to a higher energy state. Stimulated Emission:Definition: Occurs when an atom or molecule in an excited state emits a photon in response to the presence of external electromagnetic radiation. Process: The external field stimulates the already excited atom to release a photon, resulting in a transition to a lower energy state.
Einstein's relation connects the diffusion coefficient (D) with the mobility (μ) of particles in a fluid. For charged particles, the relation is given by:
D=μkBTq,D=qμkBT,
where:
- DD is the diffusion coefficient,
- μμ is the mobility of the charge carriers,
- kBkB is the Boltzmann constant,
- TT is the absolute temperature, and
- qq is the charge of the carriers.
The derivation involves considering the balance between the random thermal motion of particles (diffusion) and their drift under an electric field (mobility).
Now, regarding stimulated absorption and stimulated emission:
Difference:
- Stimulated Absorption: Energy is absorbed by the system, causing a transition to a higher energy state.
- Stimulated Emission: Energy is released by the system, leading to a transition to a lower energy state.
In summary, stimulated absorption involves the absorption of energy by a system from an external field, while stimulated emission involves the release of energy by a system in response to external radiation.
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