In one line
In spontaneous emission an excited atom drops to a lower level on its own and emits a photon in a random direction and phase, while in stimulated emission an incoming photon forces the excited atom to emit an identical photon.
Explained simply
Think of a crowd leaving a stadium. If everyone walks out whenever they feel like it, in any direction, that is spontaneous emission: random and disorganised. If a marching band walks past and people fall in step behind it, moving in the same direction at the same pace, that is stimulated emission: one photon makes another photon that is an exact copy.
Technically, an atom in an excited level \(E_2\) can return to a lower level \(E_1\) by emitting a photon of energy \(h\nu = E_2 - E_1\). If this happens without any outside trigger it is spontaneous emission. If a photon of exactly energy \(h\nu = E_2 - E_1\) passes by and triggers the transition, it is stimulated emission, and the emitted photon has the same frequency, phase, direction and polarisation as the triggering photon.
How it works
- Absorption (stimulated absorption): an atom in \(E_1\) absorbs a photon \(h\nu\) and goes to \(E_2\).
- Spontaneous emission: the excited atom stays in \(E_2\) for a short lifetime (about \(10^{-8}\) s for ordinary levels) and then drops to \(E_1\) on its own, emitting one photon in a random direction.
- Stimulated emission: before it decays on its own, a passing photon of energy \(h\nu\) forces it down; now two identical photons travel together.
- Each of these two photons can stimulate further atoms, so the light is amplified in a chain. This is the "Light Amplification by Stimulated Emission of Radiation" in the word LASER.
| Spontaneous | Stimulated |
|---|---|
| No external photon needed | Needs an incident photon of energy \(E_2-E_1\) |
| One photon out | Two identical photons out |
| Random phase and direction: incoherent | Same phase and direction: coherent |
| Light from bulbs, tube lights | Light from lasers |
| Rate depends only on \(N_2\) | Rate depends on \(N_2\) and on the photon density |
Key formula
\(h\nu = E_2 - E_1\), where \(h = 6.63\times10^{-34}\) J s is Planck's constant, \(\nu\) is the photon frequency in Hz, and \(E_2, E_1\) are the upper and lower energy levels in joules.
Quick example
A tube light glows because mercury atoms emit spontaneously, so its light spreads in all directions. A laser pointer's beam stays narrow across a room because almost all its light comes from stimulated emission.
Common mistakes
- Saying stimulated emission needs any photon. The photon energy must match \(E_2 - E_1\).
- Thinking the incident photon is absorbed in stimulated emission. It is not; it continues along with the new photon.
- Forgetting that stimulated emission dominates only when population inversion exists.
How MU asks it
Typical forms: "Differentiate between spontaneous and stimulated emission" (5 marks) or "Explain absorption, spontaneous and stimulated emission with neat diagrams" (5 marks). For full marks draw the three two-level diagrams with arrows, write \(h\nu = E_2-E_1\), and give a comparison table of at least five points.