PYQ Pattern Analysis

Pattern	Frequency	Years Appeared	Trap / Subtlety
" $V_{0}$ vs intensity" conceptual	Very High (≥5 times)	2017, 2019, 2020, 2022, 2024	$V_{0}$ does NOT change with intensity. Answer is always "unchanged."
Graph interpretation: slope of KE vs ν	High (3-4 times)	2018, 2021, 2023	Slope = h (not h/e). The $V_{0}$ vs ν slope is h/e — easily confused.
Calculate KE_max and $V_{0}$ from λ and φ	Very High	2018, 2019, 2020, 2023	Must convert λ to energy in eV using E = hc/λ or E = 1240/λ(nm) eV
de Broglie λ for electron through V	High	2021, 2022, 2024	Use λ = 1.227/√V nm. This ONLY works for electrons (m = m_e, q = e).
Electron vs proton λ comparison at same V	Moderate	2019, 2021	λ ∝ 1/√m at same V. λ_e/λ_p = √(m_p/m_e) ≈ 43.
Threshold wavelength from work function	Moderate	2018, 2022	λ_{0} = hc/φ. Use hc = 1240 eV·nm for quick calculation: λ_{0} = 1240/φ(eV) nm
Davisson-Germer conceptual	Low-Moderate	2016, 2020	Confirms wave nature of ELECTRONS (matter), not photons. Ni crystal, 54V, 50°.
Two-wavelength problem (find h and φ)	Moderate	2017, 2023	e $V_{01}$ = hν_{1} − φ and e $V_{02}$ = hν_{2} − φ → subtract to get h; then get φ

Intensity → $V_{0}$ trap: "Doubled intensity → $V_{0}$ doubles." Answer: NO. $V_{0}$ is frequency-dependent only.
Slope confusion: KE vs ν slope = h; $V_{0}$ vs ν slope = h/e. Students mix these up under pressure.
Proton shortcut trap: Using λ = 1.227/√V nm for protons/alpha particles (valid ONLY for electrons).
Frequency-doubling KE: If ν doubles, KE_max does NOT double. KE_max = h(2ν) − φ = 2hν − φ ≠ 2KE_max.
Work function units: φ must be in same units as hν when computing KE_max. If φ in eV and E in J — conversion error!

$E(\text{eV}) = \frac{1240}{\lambda(\text{nm})} \quad \text{and} \quad \lambda_0(\text{nm}) = \frac{1240}{\phi(\text{eV})}$

This avoids the long calculation with h = $6.63 \times 10^{-34}$ J s and c = $3 \times 10^{8}$ m/s.