“Brightness gives number, colour gives energy”
Intensity versus frequency
More intense light ejects more electrons but not faster ones. Higher frequency light ejects faster electrons but not more of them.
Class 12 Physics · Gujarat Board, CBSE, GUJCET, JEE and NEET
Dual Nature of Radiation and Matter formulas
This chapter is short, conceptual, and nearly free marks if the photoelectric graphs are learned. Its central point is that light arrives in packets, so intensity changes how many electrons come out and frequency changes how fast they leave.
12 formulas, 3 memory hooks, and the 5 mistakes that cost the most marks.
Photons
| What | Formula | Symbols and notes |
|---|---|---|
| Energy of a photon | E = hν = hc/λ | h = 6.626 × 10−34 J s |
| In electron volts | E (eV) = 1240/λ (nm) | the shortcut worth memorising |
| Momentum of a photon | p = h/λ = E/c | a photon has momentum but no rest mass |
| Number of photons per second | n = P/hν | P is the power of the source |
Photoelectric effect
| What | Formula | Symbols and notes |
|---|---|---|
| Einstein's equation | hν = φ₀ + KEmax | φ₀ is the work function |
| Maximum kinetic energy | KEmax = hν − φ₀ = h(ν − ν₀) | zero at the threshold frequency |
| Threshold frequency | ν₀ = φ₀/h | below this no electron comes out, however bright the light |
| Stopping potential | eV₀ = KEmax = hν − φ₀ | V₀ depends on frequency, never on intensity |
| Photocurrent | proportional to intensity | more photons means more electrons |
Matter waves
| What | Formula | Symbols and notes |
|---|---|---|
| de Broglie wavelength | λ = h/p = h/mv | every moving particle has one |
| For an accelerated electron | λ = h/√(2meV) = 12.27/√V Å | V in volts |
| For a particle at temperature T | λ = h/√(3mkT) | thermal de Broglie wavelength |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Know the formula but not when to use it?
Darshit Sir has taught this in Paldi since 2006, in the classroom and live online.
Memory hooks
How to remember this chapter.
“1240 over lambda”
Photon energy in electron volts
E in eV equals 1240 divided by the wavelength in nanometres. A 620 nm photon carries 2 eV, and the arithmetic is done.
“No delay, no threshold, no argument”
Why the wave theory failed
Emission is instantaneous, and below the threshold frequency nothing happens at all, however long you wait. Waves could explain neither.
Where marks go
The mistakes that cost the most.
- Thinking brighter light gives faster electrons. It gives more of them at the same maximum speed.
- Using the work function in joules with the frequency and then reporting electron volts, or the reverse. Fix the unit first.
- Expecting emission below the threshold frequency if you wait long enough. It never comes.
- Giving a photon a rest mass. It has energy and momentum but no rest mass.
- Forgetting that the stopping potential depends only on the frequency and the metal, never on the intensity.
Test yourself
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