Dual Nature of Radiation and Matter — Part 2: Photons, Einstein’s equation and matter waves: visual lesson, CBSE Class 12 Physics

Lesson

Photons and matter waves

Part 2 — Einstein’s packets of light explain the photoelectric effect, and de Broglie turns the idea round: particles behave as waves.

In this lesson you will

Describe the photon picture of light and apply E = hν and p = h/λ
Apply Einstein’s photoelectric equation to find work function, threshold frequency and stopping potential
Calculate the de Broglie wavelength of particles

Drawn to scale for 400 nm light on potassium (φ₀ = 2.25 eV).

Concept

The photon picture

Radiation behaves as a stream of photons, each with $E = h\nu = \dfrac{hc}{\lambda},\qquad p = \dfrac{h\nu}{c} = \dfrac{h}{\lambda}$ where $h = 6.63 \times 10^{-34}$ J s (Planck’s constant).

All photons of one frequency have the same energy; brighter light means more photons per second, not bigger photons.
Photons travel at $c$ in vacuum, have zero rest mass and are electrically neutral.
In collisions, energy and momentum are conserved; a photon can be absorbed or created.

Worked example

Worked example 3: counting photons

(a) Find the energy of a photon of 500 nm light in J and eV. (b) A 3.0 mW laser pointer emits light of wavelength 633 nm. How many photons does it emit each second?

(a) $E = \dfrac{hc}{\lambda} = \dfrac{6.63 \times 10^{-34} \times 3.0 \times 10^{8}}{500 \times 10^{-9}} \approx 3.98 \times 10^{-19}$ J $= \dfrac{3.98 \times 10^{-19}}{1.6 \times 10^{-19}} \approx 2.49$ eV.
(b) $E = \dfrac{hc}{633 \times 10^{-9}} \approx 3.14 \times 10^{-19}$ J; $N = \dfrac{P}{E} = \dfrac{3.0 \times 10^{-3}}{3.14 \times 10^{-19}} \approx 9.55 \times 10^{15}$ s $^{-1}$ .

Worked table: photon energies at 500 and 633 nanometres and the number of photons per second from a three milliwatt laser
Quantity	Value
Photon energy, 500 nm	2.49 eV
Photon energy, 633 nm	1.96 eV
Photons per second, 3.0 mW	≈ 9.5 × 10¹⁵

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