Quantum physics in NET covers black-body radiation, the photoelectric effect, Compton scattering, de Broglie waves, the hydrogen spectrum and the uncertainty principle. The single most useful shortcut for this chapter is E (in eV) = 1240 / λ (in nm). With it, most photon numericals take one division instead of three powers of ten.
Key facts
- Physics is 30% of NET-Engineering, a derived 60 of the 200 MCQs.
- Our syllabus data estimates about 6 questions from this second-year chapter.
- Syllabus: black-body radiation, the photoelectric effect, Compton scattering, de Broglie waves, atomic spectra, and Heisenberg's uncertainty principle.
Source: NUST NET-Engineering composition and the SailToNUST physics syllabus, checked October 2026
What the chapter covers
The chapter follows the history. Black-body radiation forced Planck to quantize energy. Einstein used photons to explain the photoelectric effect. Compton showed photons carry momentum. De Broglie gave matter a wavelength, and Bohr's model explained the hydrogen spectrum. The uncertainty principle closes the chapter. NET draws both one-line concept questions and short numericals from every part.
Formulas you need
Photon energy E = hf = hc/λ h = 6.63 × 10⁻³⁴ J s
Shortcut E (eV) = 1240 / λ (nm)
Photon momentum p = h/λ = E/c
1 eV = 1.6 × 10⁻¹⁹ J
Black body
Wien's law λ_max T = 2.9 × 10⁻³ m K
Stefan's law E = σT⁴ σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴
Photoelectric effect hf = φ + K_max
K_max = eV₀ (V₀ = stopping potential)
threshold frequency f₀ = φ/h
Compton shift Δλ = (h / m₀c)(1 − cosθ)
h / m₀c = 2.43 × 10⁻¹² m (Compton wavelength)
de Broglie λ = h/p = h/mv = h/√(2mK)
electron through V volts λ ≈ 1.23/√V nm
Hydrogen (Bohr) Eₙ = −13.6/n² eV, rₙ = n² × 0.053 nm
Spectral lines 1/λ = R_H (1/n₁² − 1/n₂²), R_H = 1.097 × 10⁷ m⁻¹
Series ending on n₁: 1 Lyman (UV), 2 Balmer (visible), 3 Paschen,
4 Brackett, 5 Pfund (infrared)
X-ray tube cut-off λ_min = hc / eV
Pair production needs at least 1.02 MeV
Uncertainty Δx Δp ≥ h/4π (your textbook may write Δx Δp ≈ h)
Worked MCQs
1. X-ray cut-off wavelength. An X-ray tube runs at 30 kV. What is the shortest wavelength it emits?
(a) 2840 Å (b) 0.413 Å (c) 2.14 Å (d) 1.78 Å
Photon energy max = 30 keV = 30,000 eV
λ_min = 1240 / 30,000 nm = 0.0413 nm = 0.413 Å
Answer (b). 1 nm is 10 Å, which is the conversion people forget at the last step.
2. Stopping potential. Light of wavelength 300 nm falls on a metal with work function 2.5 eV. What is the stopping potential?
(a) 4.13 V (b) 2.5 V (c) 1.63 V (d) 6.63 V
E = 1240 / 300 = 4.13 eV
K_max = 4.13 − 2.5 = 1.63 eV
V₀ = 1.63 V
Answer (c). In electron-volts, K_max and the stopping potential have the same number. That saves a conversion.
3. Compton angle. The Compton shift equals half the Compton wavelength. What is the scattering angle?
(a) 30° (b) 60° (c) 90° (d) 120°
Δλ = (h/m₀c)(1 − cosθ) = ½ (h/m₀c)
1 − cosθ = ½ so cosθ = ½ so θ = 60°
Answer (b). The shift is largest at 180°, where it equals twice the Compton wavelength.
4. The red hydrogen line. An electron in hydrogen drops from n = 3 to n = 2. What wavelength is emitted?
(a) 122 nm (b) 486 nm (c) 656 nm (d) 1875 nm
ΔE = 13.6 (1/4 − 1/9) = 13.6 × 5/36 ≈ 1.89 eV
λ = 1240 / 1.89 ≈ 656 nm
Answer (c). It ends on n = 2, so it belongs to the Balmer series and is visible red light. 122 nm is the first Lyman line (2 to 1). 1875 nm is the first Paschen line (4 to 3).
5. Electron wavelength. An electron is accelerated from rest through 100 V. What is its de Broglie wavelength?
(a) 0.0123 nm (b) 0.123 nm (c) 1.23 nm (d) 12.3 nm
λ = h / √(2meV)
= 6.63 × 10⁻³⁴ / √(2 × 9.11 × 10⁻³¹ × 1.6 × 10⁻¹⁹ × 100)
= 6.63 × 10⁻³⁴ / 5.4 × 10⁻²⁴ ≈ 1.23 × 10⁻¹⁰ m = 0.123 nm
Answer (b). With the shortcut, 1.23/√100 = 0.123 nm in one line. That is about the spacing of atoms in a crystal, which is why electron diffraction works.
Traps that cost marks
- Intensity versus frequency. Brighter light gives more photoelectrons, not faster ones. K_max depends only on frequency. Below the threshold frequency, no intensity will release a single electron.
- Compton shift does not depend on the incident wavelength or the target material. It depends only on the angle.
- Comparing de Broglie wavelengths. At the same speed, the lightest particle has the longest wavelength, so an electron beats a proton or an alpha. At the same kinetic energy, λ ∝ 1/√m, so the order is the same but the ratios differ. Read which quantity is fixed.
- A black body is an ideal absorber and an ideal emitter. It is not black when hot. The Sun is a near black body.
- Wien's law and colour. Hotter bodies peak at shorter wavelengths. A star that looks blue is hotter than one that looks red.
- Your body radiates infrared. At about 310 K, Wien's law puts the peak near 9.4 μm.
- Photon energy doubles when frequency doubles. E ∝ f and E ∝ 1/λ.
Speed tips for the exam
Memorise 1240 eV nm. It turns every photon-energy question into a single division, and 1240/620 = 2 eV and 1240/400 = 3.1 eV give you quick anchors for red and violet light.
For hydrogen, learn the first few energy levels: −13.6, −3.4, −1.51 and −0.85 eV for n = 1 to 4. The energy of any transition is a subtraction.
For de Broglie ratio questions, write λ ∝ 1/√(mK) or λ ∝ 1/√(mqV) as the question demands, and scale.
The wave side of light is in physical optics. The nucleus, where the next chapter goes, is in nuclear physics.
FAQ
What is the work function?
The minimum energy needed to free an electron from a metal surface. It is usually given in electron-volts and differs from metal to metal.
Which hydrogen series is visible?
The Balmer series, for transitions ending on n = 2. Lyman is ultraviolet, and Paschen, Brackett and Pfund are infrared.
Why does Compton scattering prove photons have momentum?
The scattered X-ray has a longer wavelength, and the shift matches a billiard-ball collision between a photon of momentum h/λ and a free electron. A pure wave picture cannot explain that shift.
Is quantum physics important for NET?
Our syllabus estimate puts it at about 6 of the derived 60 physics MCQs. The question types repeat, so it is one of the better chapters to drill late in your prep.
