Dawn of Modern Physics

Classical physics treated light purely as a wave. In 1900 Planck showed that radiation is emitted and absorbed in discrete packets of energy, and modern physics began. The PMDC MDCAT 2026 syllabus reduces this whole chapter to a single subtopic — "Quantum Theory and Radiation" — with one learning outcome: explain the particle model of light in terms of photons with energy.

PMC Table of Specifications. Quantum Theory and Radiation is the single listed subtopic, and the single learning outcome (14.1) is to explain the particle model of light in terms of photons with energy. Everything you need sits on the equation E = hf.

Quantum Theory and Radiation

Quantum theory says that electromagnetic radiation is not a continuous stream of energy. It comes in indivisible packets called quanta, and a single quantum of light is called a photon. This is the particle model of light.

Planck's quantum hypothesis (1900)

Planck proposed that radiation is emitted and absorbed only in discrete packets, each carrying an energy fixed by the frequency of the radiation:

E = hf = hc/λ

where h = 6.626 × 10⁻³⁴ J s is Planck's constant, c = 3.0 × 10⁸ m s⁻¹, f is the frequency and λ the wavelength. This one equation is the foundation of quantum theory and is the most-tested relation in the chapter.

The photon

A photon is one quantum of electromagnetic radiation — the "particle" of light. Its properties:

Energy E = hf = hc/λ. Energy is directly proportional to frequency and inversely proportional to wavelength, so gamma rays carry far more energy per photon than radio waves.
Zero rest mass, no electric charge, and it always travels at the speed of light c in vacuum.
It carries momentum p = E/c = h/λ, which is why a beam of light exerts a small radiation pressure.
Energy is quantised: a source cannot emit half a photon. If a source emits n photons per second, the beam power is P = nhf.

Common trap. A brighter beam is not a more energetic photon. Raising the intensity raises the number of photons emitted per second; the energy of each individual photon depends on frequency alone. This is the single most-tested fact in the chapter.

Photon energy in joules and electron volts

MDCAT numericals quote photon energies in either joules or electron volts, where 1 eV = 1.602 × 10⁻¹⁹ J. A shortcut worth memorising:

hc = 1240 eV nm → E (in eV) = 1240 / λ (in nm)

Worked example 1. Green light of wavelength 500 nm: E = 1240/500 = 2.48 eV, i.e. 2.48 × 1.602 × 10⁻¹⁹ = 3.97 × 10⁻¹⁹ J.
Worked example 2. A photon of frequency 6.0 × 10¹⁴ Hz: E = hf = (6.626 × 10⁻³⁴)(6.0 × 10¹⁴) = 3.98 × 10⁻¹⁹ J ≈ 2.48 eV — the same photon, since λ = c/f = 500 nm.

Wave-particle duality of light

Light behaves sometimes as a wave (interference, diffraction, refraction) and sometimes as a stream of particles (photons carrying energy hf and momentum h/λ). The two pictures are complementary, not contradictory — the experiment you perform decides which face of light appears.

Mnemonic for the constants. Memorise just two numbers and derive the rest: h = 6.626 × 10⁻³⁴ J s and 1 eV = 1.602 × 10⁻¹⁹ J. From these you can convert any photon energy from joules to eV (divide by 1.6 × 10⁻¹⁹) and back.

Worked MCQs

Five MCQs that capture the high-yield testing patterns for this chapter. Read the explanation even when you get the answer right — it's where the deeper concept lives.

Q1. The energy of a photon of wavelength 620 nm is approximately:

1.0 eV
2.0 eV
3.1 eV
6.2 eV

Using hc = 1240 eV nm, E = 1240/620 = 2.0 eV. In joules that is 2.0 × 1.602 × 10⁻¹⁹ = 3.2 × 10⁻¹⁹ J.

Q2. If the frequency of a monochromatic source is doubled, the energy carried by each photon:

Is halved
Remains unchanged
Is doubled
Becomes four times larger

E = hf, so photon energy is directly proportional to frequency. Equivalently, doubling the frequency halves the wavelength and E = hc/λ doubles.

Q3. The momentum of a photon of wavelength λ is given by:

hλ
h/λ
hc/λ
λ/h

A photon has zero rest mass but carries momentum p = E/c = (hc/λ)/c = h/λ. Note hc/λ is the photon's energy, not its momentum — a favourite distractor.

Q4. Increasing the intensity of a monochromatic light beam increases:

The energy of each photon
The number of photons emitted per second
The speed of the photons
The wavelength of the light

Beam power P = nhf. For fixed frequency, more intensity simply means a larger n. Photon energy hf and photon speed c are both unchanged.

Q5. The energy of a photon of frequency 5.0 × 10¹⁴ Hz is closest to:

3.3 × 10⁻²⁰ J
3.3 × 10⁻¹⁹ J
1.3 × 10⁻¹⁹ J
7.5 × 10⁻¹⁹ J

E = hf = (6.626 × 10⁻³⁴)(5.0 × 10¹⁴) = 3.31 × 10⁻¹⁹ J, which is about 2.07 eV.

Quick Recap

A photon is one quantum of electromagnetic radiation — the particle of light.
Planck: E = hf = hc/λ, with h = 6.626 × 10⁻³⁴ J s.
Photon momentum p = E/c = h/λ; rest mass is zero and speed is always c in vacuum.
Intensity → number of photons per second; frequency → energy of each photon.
Beam power P = nhf for n photons per second.
Useful conversions: hc = 1240 eV nm and 1 eV = 1.602 × 10⁻¹⁹ J.
Light is complementary: wave behaviour in interference/diffraction, particle behaviour as photons.

Test yourself. Take a timed Modern Physics quiz or browse all Physics MCQs to lock these concepts in.