Photon Rate, Power, and Energy Density
For monochromatic radiation, total energy is the number of photons times h nu. Power is energy per unit time, so the photon emission rate equals power divided by single-photon energy.
Why this shows up in the exam
Estimating laser photon output · Comparing photon counts from equal-power sources · Converting photon number density to electromagnetic energy density
Learn the idea
Optical power counts photon energy delivered per unit time, not photons alone. A beam with fixed power can contain many low-energy photons or fewer high-energy photons. Counting photons therefore requires both the beam power and the energy carried by each photon.
🧠 Memory hook: Photon rate equals power divided by energy per photon.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- P = N_dot h nu = N_dot h c / lambda — power of a monochromatic source emitting N_dot photons per second
- u = n h nu — energy density when n is the number of equal-frequency photons per unit volume
How to approach it
- 1Calculate one photon energy from wavelength or frequency
- 2Write power as photon rate times photon energy
- 3Cancel constants before inserting numerical values in ratios
Common slip-ups that cost marks
- •Assuming equal powers imply equal photon rates at different wavelengths
- •Using total photon number where photons per second are required
- •Forgetting that longer wavelength means smaller energy per photon
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
Photons of energy 5 eV illuminate a metal of work function 2 eV. Find the stopping potential.
More from Dual Nature of Matter and Radiation
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Photons are massless particles of light characterized by their energy, frequency, momentum, and charge neutrality, and their interactions obey conservation laws.
Photon Energy and Momentum
For a photon in vacuum, energy is proportional to frequency and momentum is energy divided by c. Frequency and wavelength obey c = nu lambda, so shorter-wavelength photons have larger energy and momentum.
Radiation Pressure and Photon Momentum Transfer
Radiation force is the rate of photon momentum transfer. For normal incidence on an ideal absorber the pressure is intensity divided by c; for an ideal reflector it is twice that value.
Photoelectric Effect Observations
For a fixed emitter, emission occurs only when incident frequency reaches the threshold frequency. Above threshold, maximum kinetic energy depends on frequency, while saturation current is primarily proportional to intensity.