Energy levels, absorption and emission
Electrons in an atom can only have certain energies, called energy levels. To jump up, an electron must take in exactly the energy difference ΔE. To come down, it gives out a photon with energy E = hf = ΔE.
- Absorption: a photon is taken in; the atom becomes excited.
- Spontaneous emission: the excited atom drops back on its own, at a random time, in a random direction.
A normal bulb gives light by spontaneous emission, so its light goes everywhere and has many colours.
Stimulated emission
Einstein predicted in 1917 that a photon with energy ΔE passing an excited atom can trigger it to drop down early. The new photon is an exact copy: same frequency (colour), same direction and same phase (the waves rise and fall together). One photon becomes two, two become four, and the light is amplified.
Population inversion and the laser cavity
Normally most atoms are in the lowest level, so photons are absorbed more often than they are copied. A pump (a flash lamp, an electric current or another laser) puts energy in so that more atoms are excited than not. This is population inversion. Many lasers use a metastable level where atoms stay excited a little longer.
The cavity has a full mirror at one end and a partial mirror at the other. Light bouncing along the axis keeps being amplified; light going sideways is lost. A small part leaks out through the partial mirror as the beam.
Properties and uses of laser light
- Monochromatic: one colour (one wavelength).
- Coherent: all waves in step.
- Directional: very narrow beam that hardly spreads.
- Intense: energy packed into a tiny spot.
Uses: surgery and eye correction, barcode scanners, optical fibre communication, cutting and welding, measuring distance (lidar), holograms, reading discs.
Safety: never look into a laser beam. Even a small pointer can damage the eye’s retina.
X-rays
X-rays are electromagnetic waves of very short wavelength (about 0.01–10 nm) and high photon energy. In an X-ray tube, electrons are sped up by a high voltage and hit a metal target. They slow down suddenly and give out X-rays (braking radiation), and they also knock out inner electrons, giving sharp "characteristic" lines. X-rays pass through soft tissue but are stopped more by bone, which is why they show bones. They ionise matter, so exposure is kept small and lead shields are used.
Laser light and X-rays are both photons; they differ in energy and in how they are made.
Try it: see the difference
In a dark room, shine a torch and a laser pointer (pointed at a wall, never at eyes) from 3 m away. Compare the spot sizes. The torch spreads widely; the laser stays a small dot. Then use the pump slider in the 3D: find the lowest pump level that still gives a beam.
Key formulas and definitions
- E = hf = hc/λ
- ΔE = E₂ − E₁ (photon energy = gap between levels)
- h = 6.63 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s
- 1 eV = 1.6 × 10⁻¹⁹ J
- Shortest X-ray wavelength: λmin = hc/(eV)
Worked examples
1. A red laser has λ = 650 nm. Find the energy of one photon.
E = hc/λ = (6.63 × 10⁻³⁴ × 3 × 10⁸) / (650 × 10⁻⁹) = 3.06 × 10⁻¹⁹ J ≈ 1.9 eV.
2. Two levels differ by 2.0 eV. What wavelength does a stimulated photon have?
ΔE = 2.0 × 1.6 × 10⁻¹⁹ = 3.2 × 10⁻¹⁹ J. λ = hc/ΔE = 1.99 × 10⁻²⁵ / 3.2 × 10⁻¹⁹ = 6.2 × 10⁻⁷ m = 620 nm (orange-red).
3. A 1 mW laser gives photons of 3.0 × 10⁻¹⁹ J. How many photons per second?
N = P/E = 1 × 10⁻³ / 3.0 × 10⁻¹⁹ = 3.3 × 10¹⁵ photons each second.
4. An X-ray tube works at 30 kV. Find the shortest X-ray wavelength.
Maximum photon energy = eV = 1.6 × 10⁻¹⁹ × 30000 = 4.8 × 10⁻¹⁵ J. λmin = hc/E = 1.99 × 10⁻²⁵ / 4.8 × 10⁻¹⁵ = 4.1 × 10⁻¹¹ m = 0.041 nm.
Common mistakes
- Thinking stimulated emission makes a photon of a different colour: the copy has the same frequency, phase and direction.
- Forgetting population inversion: without it, absorption wins and there is no amplification.
- Saying laser light is "stronger" only because of power: the key is coherence and narrow direction.
- Mixing eV and joules: multiply eV by 1.6 × 10⁻¹⁹ to get joules.