Dawn of Modern Physics

By 1900 classical physics could not explain blackbody radiation, the photoelectric effect, or atomic stability. The breakthroughs of Planck, Einstein, Bohr, de Broglie, and Compton ushered in modern physics. The PMDC MDCAT 2026 syllabus packs all this into a single subtopic — "Quantum Theory and Radiation" — that yields a steady stream of MCQs every year.

PMC Table of Specifications. Quantum Theory and Radiation is the single listed subtopic, but it bundles Planck's hypothesis, the photoelectric effect, Compton effect, de Broglie waves, blackbody radiation, and the Rutherford/Bohr atomic models.

Quantum Theory and Radiation

The classical Rayleigh-Jeans law predicted infinite radiation at short wavelengths — the so-called "ultraviolet catastrophe." Experiments showed instead a peak at a finite wavelength.

Blackbody radiation

A blackbody is a perfect absorber and emitter. Its spectrum depends only on temperature.
Stefan-Boltzmann law: total power emitted per unit area E = σT⁴, with σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴.
Wien's displacement law: λ_max T = b, with b = 2.898 × 10⁻³ m K. Hotter bodies emit at shorter wavelengths.

Planck's quantum hypothesis (1900)

To fit the blackbody curve, Planck proposed that radiation is emitted/absorbed in discrete packets called quanta:

E = hf = hc/λ

where h = 6.626 × 10⁻³⁴ J s is Planck's constant. This was the foundational idea that begins quantum mechanics.

Photoelectric effect

When light of sufficiently high frequency strikes a metal surface, electrons are ejected immediately. Classical wave theory could not explain four observations:

A threshold frequency f₀ exists below which no electrons are ejected, no matter how intense the light.
Maximum kinetic energy of photoelectrons is independent of intensity but increases linearly with frequency.
Photoelectrons appear instantaneously (no time lag).
Number of electrons (i.e. current) is proportional to intensity.

Einstein (1905) explained the effect using Planck's quanta — light behaves as discrete photons of energy hf. Each photon ejects one electron:

hf = φ + KE_max

where φ = h f₀ is the work function of the metal (minimum energy to free an electron). Therefore KE_max = hf − φ.

Experimentally, KE_max is measured by applying a reverse stopping potential V_s until the photocurrent just falls to zero: eV_s = KE_max.

Common trap. Increasing the intensity of light increases the number of photoelectrons (current) but not their kinetic energy. To raise KE_max you must raise the frequency. This is the most-tested fact in modern physics.

Compton effect

When X-ray photons scatter off loosely bound electrons, the scattered radiation has a longer wavelength than the incident. This proves that photons carry both energy and momentum.

Δλ = λ' − λ = (h/m_ec)(1 − cosθ)

The factor h/(m_ec) = 2.43 × 10⁻¹² m is the Compton wavelength of the electron. Δλ is independent of the incident wavelength — it depends only on the scattering angle.

Photoelectric effect vs Compton effect vs Pair production
Property	Photoelectric	Compton	Pair production
Photon energy range	UV / visible (eV)	X-ray (~keV)	> 1.022 MeV (gamma)
Target electron	Tightly bound (in metal)	Loosely bound / free	Nucleus (needs electric field)
Photon fate	Absorbed entirely	Scattered with lower energy (longer λ)	Disappears, becomes e⁻ + e⁺
Outcome	Electron ejected from metal	Scattered photon + recoiling electron	Electron-positron pair
Key equation	hf = φ + KE_max	Δλ = (h/m_ec)(1 − cosθ)	hν ≥ 2m_ec² (= 1.022 MeV)
Threshold	f ≥ f₀ = φ/h	None (any X-ray scatters)	1.022 MeV minimum photon energy
Demonstrates	Particle nature of light, quantisation	Photon momentum p = h/λ	Mass-energy equivalence E = mc²

de Broglie wavelength — matter waves

If light has particle properties, particles should have wave properties. Louis de Broglie (1924) proposed:

λ = h/p = h/(mv)

This was confirmed by the Davisson-Germer electron diffraction experiment (1927). Macroscopic objects have unmeasurably tiny λ (e.g. 10⁻³⁴ m for a cricket ball); only microscopic particles show wave behaviour.

Wave-particle duality

Light and matter both behave sometimes as waves (interference, diffraction) and sometimes as particles (photoelectric effect, Compton scattering). The two pictures are complementary, not contradictory — the experiment chooses which face appears.

Atomic models — Rutherford to Bohr

Rutherford (1911): α-particle scattering experiment showed atoms are mostly empty space with a tiny, dense, positively charged nucleus. Electrons orbit the nucleus.
Failure: Classical physics says an orbiting electron should radiate energy and spiral into the nucleus — atoms would not be stable.
Bohr (1913): Quantised the orbits using mvr = nh/(2π), restored stability, and explained the hydrogen line spectrum. E_n = −13.6/n² eV.

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 maximum kinetic energy of photoelectrons depends on:

Intensity of incident light only
Frequency of incident light and work function
Intensity and angle of incidence
Surface area of the metal only

From Einstein's equation KE_max = hf − φ. Intensity changes the number of photoelectrons (current), not their energy. The threshold frequency f₀ = φ/h is set by the metal.

Q2. The de Broglie wavelength of a particle of mass m and kinetic energy E is:

h/(mE)
h/√(2mE)
hE/m
√(2hE/m)

For a non-relativistic particle p = √(2mE), so λ = h/p = h/√(2mE). This is the standard form used in MCQs about electrons accelerated through a potential V (where E = eV).

Q3. Wien's displacement law states that as the temperature of a blackbody rises:

Total radiated power decreases
Peak wavelength stays constant
Peak wavelength becomes shorter
The body becomes a perfect reflector

λ_max T = b. As T ↑, λ_max ↓ — that's why a heated iron rod glows red, then orange, then white as it gets hotter. Total power E = σT⁴ rises sharply as well.

Q4. The Compton shift Δλ in a scattering experiment depends on:

Wavelength of incident X-rays
Scattering angle θ
Intensity of incident beam
Material of the scatterer

Δλ = (h/m_ec)(1 − cosθ). It is zero at θ = 0°, maximum at θ = 180°, and independent of incident λ or intensity. This was the strongest evidence that photons carry momentum p = h/λ.

Q5. The work function of a metal is 2 eV. The threshold wavelength is approximately:

310 nm
620 nm
1240 nm
62 nm

A useful conversion: hc = 1240 eV nm. Threshold wavelength λ₀ = hc/φ = 1240/2 = 620 nm (orange light). For most common metals φ falls in 2-5 eV, so threshold is in the visible-UV region.

Quick Recap

Planck: E = hf = hc/λ.
Photoelectric: KE_max = hf − φ; threshold f₀ = φ/h; eV_s = KE_max.
Intensity → number of electrons; frequency → their energy.
Compton: Δλ = (h/m_ec)(1 − cosθ); proves photon momentum.
de Broglie: λ = h/p; verified by electron diffraction.
Stefan: E = σT⁴. Wien: λ_max T = b.
Rutherford = nuclear atom. Bohr = quantised orbits, E_n = −13.6/n² eV.
Useful: hc = 1240 eV nm.

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