Error Analysis — Common Mistakes in PH-01 — Notes

#	Mistake	Why Students Make It	Correct Understanding	Correct Formula/Fact
1	"Doubling intensity doubles $V_{0}$ "	Confusing intensity with energy per photon	$V_{0}$ depends only on ν, not intensity	$V_{0}$ = (hν − φ)/e; intensity does NOT appear
2	"Below ν_{0}, emission occurs at very high intensity"	Thinking more photons = enough energy	Energy is quantised; 1 photon → 1 electron; each photon must individually exceed φ	No emission if hν < φ, regardless of intensity
3	"λ = 1.227/√V works for protons too"	Forgetting the formula derivation uses m_e	Derived specifically for electrons: λ = h/√(2m_e eV)	Use λ = h/√(2mpeV) for protons; numerically different
4	"Slope of $V_{0}$ vs ν graph is h"	Confusing with KE vs ν graph	$V_{0}$ = (h/e)ν − φ/e; slope = h/e, not h	Slope of KE_max vs ν = h; slope of $V_{0}$ vs ν = h/e
5	"KE_max doubles when frequency doubles"	Applying simple proportionality	KE_max = hν − φ; not a direct proportion because of the −φ term	New KE_max = h(2ν) − φ = 2hν − φ ≠ 2(hν − φ) unless φ = 0
6	"Photon has mass m = E/ $c^{2}$ "	Applying E = m $c^{2}$ directly	Photons have zero REST mass; E = pc for massless particles	m_{0} = 0; relativistic mass concept should not be used here
7	"At same velocity, λ_e = λ_p because charge is same"	Thinking charge affects de Broglie wavelength	λ = h/(mv); charge plays no role. Only mass and velocity matter	λ_e/λ_p = m_p/m_e ≈ 1836 at same velocity
8	"Saturation current is the same for different intensities"	Misreading the I vs V graph description	Different intensities → different saturation currents; same $V_{0}$ (stopping potential)	I_sat ∝ intensity; $V_{0}$ independent of intensity
9	"Threshold frequency is different for the same metal under different conditions"	Thinking temperature or surface condition changes ν_{0}	ν_{0} = φ/h; for a pure metal, φ is fixed, so ν_{0} is fixed. Surface oxidation changes φ	ν_{0} depends ONLY on the work function of the specific metal
10	"Work function is in Hz (frequency units)"	Confusing φ with ν_{0}	φ is energy [ $ML^{2}$$T^{-2}$ ]; ν_{0} is frequency [ $T^{-1}$ ]; φ = hν_{0}	φ in J or eV; ν_{0} in Hz; φ = hν_{0} connects them