Home/MDCAT/Physics/Dawn of Modern Physics
Chapter 15 of 16 · Physics
Dawn of Modern Physics
Dawn of Modern Physics averages 3 MCQs per paper — photoelectric effect, Compton, de Broglie, and Bohr atom dominate.
Dawn of Modern Physics is a Physics chapter on the official PMDC MDCAT 2026 syllabus, contributing roughly 3 MCQs to the 36-MCQ Physics section. Mastering the core concepts below typically secures the full chapter weightage.
Black-body radiation and Planck's quantum
Classical theory failed catastrophically at high frequencies (the ultraviolet catastrophe). In 1900 Planck proposed E = nhf with h = 6.626×10⁻³⁴ J·s, fitting the spectrum exactly. Wien's displacement law: λmax·T = 2.898×10⁻³ m·K. Stefan-Boltzmann: total radiated power per area is σT⁴, with σ = 5.67×10⁻⁸ W/(m²·K⁴). The Sun's λmax ≈ 500 nm gives surface T ≈ 5800 K.
Photoelectric effect
Einstein 1905: light delivers energy in quanta. The equation hf = φ + ½mv²max, where φ is the work function, explains: (1) instantaneous emission, (2) threshold frequency f₀ = φ/h below which no current flows regardless of intensity, (3) maximum KE depends on f, not intensity. Stopping potential Vs satisfies eVs = ½mv²max. For sodium, φ ≈ 2.3 eV, so f₀ ≈ 5.6×10¹⁴ Hz (visible green region).
Compton scattering
Compton 1923 demonstrated photon-momentum behaviour: X-rays scattering off electrons shift in wavelength by Δλ = (h/mec)(1 − cos θ), where the Compton wavelength of the electron h/mec ≈ 2.43×10⁻¹² m. Maximum shift is at θ = 180°, giving 2λC. This finally established photons as carriers of momentum p = h/λ.
de Broglie matter waves and Bohr atom
de Broglie 1924: every particle has wavelength λ = h/p. An electron accelerated through 100 V has λ ≈ 0.123 nm, comparable to atomic spacings — confirmed by Davisson-Germer's 1927 diffraction experiment. Bohr's model (1913): angular momentum quantised as L = nℏ; radii rn = n²·a₀ with a₀ = 0.529 Å; energy En = −13.6/n² eV (hydrogen). Lyman series ends on n=1 (UV), Balmer on n=2 (visible), Paschen on n=3 (IR).
Special relativity briefly
Two postulates: (1) physical laws are the same in all inertial frames, (2) the speed of light c = 3×10⁸ m/s is constant in all frames. Consequences: time dilation Δt = γΔt₀, length contraction L = L₀/γ, mass-energy E = γmc² with rest energy mc². Lorentz factor γ = 1/√(1−v²/c²). At v = 0.6c, γ = 1.25; at 0.8c, γ = 5/3. References: HRW Chapters 37-39, Serway Modern Physics, FSc Chapters 19-20.
Key Concepts
- Photoelectric effect
- Compton scattering
- de Broglie wavelength
- Heisenberg uncertainty
- Special relativity basics
Worked MCQs
Q1. Work function of a metal is 2 eV. Threshold frequency is approximately:
- A. 2.4×10¹⁴ Hz
- B. 4.8×10¹⁴ Hz ✓
- C. 5.0×10¹⁴ Hz
- D. 1.2×10¹⁵ Hz
Explanation: f₀ = φ/h = 2·1.6×10⁻¹⁹/6.626×10⁻³⁴ ≈ 4.83×10¹⁴ Hz.
Common trap: Forgetting to convert eV to joules.
Q2. de Broglie wavelength of an electron with KE = 100 eV is approximately:
- A. 0.012 nm
- B. 0.123 nm ✓
- C. 1.23 nm
- D. 12.3 nm
Explanation: λ = h/√(2mKE) ≈ 0.123 nm using m_e = 9.11×10⁻³¹ kg.
Common trap: Off by orders of magnitude when units (eV → J) are not converted.
Q3. Energy of the n=2 level in hydrogen is:
- A. −13.6 eV
- B. −6.8 eV
- C. −3.4 eV ✓
- D. −1.51 eV
Explanation: E_n = −13.6/n² = −13.6/4 = −3.4 eV.
Common trap: Choosing −6.8 eV — that would be −13.6/2, not /n².
Q4. Compton wavelength of the electron is:
- A. 2.43×10⁻¹⁰ m
- B. 2.43×10⁻¹² m ✓
- C. 1.21×10⁻¹⁰ m
- D. 9.11×10⁻³¹ m
Explanation: λ_C = h/(m_e·c) ≈ 2.43×10⁻¹² m.
Common trap: Confusing Compton wavelength with Bohr radius.
Q5. If a particle's speed is 0.6c, its Lorentz factor γ is:
- A. 1.0
- B. 1.25 ✓
- C. 1.5
- D. 2.0
Explanation: γ = 1/√(1 − 0.36) = 1/√0.64 = 1/0.8 = 1.25.
Common trap: Using 1/(1−v/c) gives 2.5.
Frequently Asked Questions
Why does the photoelectric effect violate the wave model?
Wave theory predicts emission depending on intensity and being delayed; observation shows threshold frequency and instantaneous emission, which only quanta can explain.
Did Einstein win the Nobel for relativity?
No — he won the 1921 Nobel Prize for the photoelectric effect, not relativity.
Why is Bohr's model considered semi-classical?
It mixes classical orbits with an ad-hoc quantisation of angular momentum, lacking the wave-mechanical justification provided later by Schrödinger.
What is the Compton shift's significance?
It established that photons carry momentum p = h/λ, completing the wave-particle duality of light.
Does mass really increase with speed?
Modern usage prefers fixed rest mass m and writes E = γmc². The 'relativistic mass' γm is a pedagogical device, not a fundamental quantity.
How Dawn of Modern Physics Is Tested
MDCAT questions on Dawn of Modern Physics are a mix of recall (definitions, classifications), application (predict outcomes, interpret diagrams), and basic numerical/analytical reasoning. PMDC papers from 2020–2025 emphasized the concepts above; older UHS papers (2008–2019) tested them too, with slight variations in question framing.
Practice
Drill Dawn of Modern Physics and the rest of Physics — free, no signup.
See the full MDCAT 2026 syllabus or browse all Physics chapters.