Physics · Dual Nature Of Radiation And Matter · NEET
The longest wavelength that can cause photoemission is the threshold wavelength (lambda-0). It is the wavelength whose photon energy exactly equals the metal's work function, so lambda-0 = hc / phi. Using hc = 1240 eV.nm, just do lambda-0 (in nm) = 1240 / phi (in eV). Memory hook: "Longest wavelength = weakest photon that still just barely works." Any wavelength longer than lambda-0 has a weaker photon and cannot eject an electron.
The threshold wavelength lambda-0 = hc/phi is the longest wavelength that still causes photoemission. Shorter wavelengths (left, higher energy) eject electrons; longer wavelengths (right, lower energy) do not, no matter the intensity.
Your doubts, answered
Why is the LONGEST wavelength (not shortest) the limit for photoemission?
Photon energy is E = hc/lambda. Energy goes DOWN as wavelength goes UP. So a long wavelength means a weak photon. To eject an electron the photon needs at least the work function phi. The longest wavelength that still supplies exactly phi is the limit; go any longer and the photon is too weak. That limit wavelength is the threshold wavelength lambda-0.
What is the quick formula in nm?
Set photon energy equal to work function: hc/lambda-0 = phi. So lambda-0 = hc/phi. Using the shortcut hc = 1240 eV.nm, lambda-0 (nm) = 1240 / phi (eV). Example: phi = 4.0 eV gives lambda-0 = 1240/4.0 = 310 nm.
Does a longer wavelength carry more or less energy?
Less energy. E = hc/lambda, so wavelength and energy are inversely related. Long wavelength (red, infrared) = low energy photon. Short wavelength (blue, ultraviolet) = high energy photon. This is why UV causes photoemission easily but red light often does not.
Threshold frequency vs threshold wavelength: are they the same idea?
Yes, they describe the same limit from two sides. Threshold frequency nu-0 is the MINIMUM frequency that works (phi = h.nu-0). Threshold wavelength lambda-0 is the MAXIMUM (longest) wavelength that works. They are linked by lambda-0 = c/nu-0. Emission needs nu greater than nu-0, which is the same as lambda less than lambda-0.
If the incident wavelength is longer than lambda-0, will any electrons come out?
No. If lambda is greater than lambda-0, the photon energy hc/lambda is less than phi. Increasing the intensity (more photons) does not help, because each single photon is still too weak. Zero electrons are emitted, no matter how bright the light.
How do I find the maximum wavelength that causes the photoelectric effect in a problem?
Maximum wavelength = threshold wavelength. Take the work function phi (convert to eV if needed) and compute lambda-0 = 1240/phi nm. If phi is given in joules, use lambda-0 = hc/phi with h = 6.6x10^-34 J.s and c = 3x10^8 m/s.
⚠️ The NEET trap ✗ Reading 'longest wavelength' as the SHORTEST wavelength, or thinking emission happens when lambda is greater than lambda-0. ✓ Longest wavelength that works = threshold wavelength lambda-0 = hc/phi. Emission happens only when lambda is LESS than or equal to lambda-0 (photon energy at or above phi). 🧠 Long wavelength = weak photon. The longest wavelength that STILL works is the threshold. Longer than that = too weak = no electrons.
Real NEET questions
NEET 2019 (Odisha)
The work function of a photosensitive material is 4.0 eV. The longest wavelength of light that can cause photoemission from the substance is (approximately):
A · 3100 nm
B · 966 nm
C · 31 nm
D · 310 nm ✓
Solution: Longest wavelength = threshold wavelength lambda-0 = hc/phi. Using hc = 1240 eV.nm: lambda-0 = 1240 / 4.0 = 310 nm. Any wavelength longer than 310 nm has photon energy below 4.0 eV and cannot emit electrons. Answer: 310 nm (D).
NEET 2026 (Phase 1)
For a metal of work function 6.6 eV, which of the following wavelengths of incident radiation does NOT give rise to the photoelectric effect? (Take Planck's constant as 6.6 x 10^-34 J.s)
A · 100 nm
B · 150 nm
C · 200 nm ✓
D · 50 nm
Solution: First find the threshold (longest usable) wavelength. lambda-0 = hc/W = (6.6x10^-34 x 3x10^8) / (6.6 x 1.6x10^-19) = 1.875x10^-7 m = 187.5 nm. Emission needs lambda less than lambda-0 = 187.5 nm. Among the options, 200 nm is greater than 187.5 nm, so its photon is too weak: no photoelectric effect. Answer: 200 nm (C).
Solved Dual Nature Of Radiation And Matter NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the longest wavelength that causes photoemission?
It is the threshold wavelength lambda-0, given by lambda-0 = hc/phi, where phi is the work function. In nm it is simply 1240/phi(eV). Longer wavelengths cannot cause emission.
What is the formula for the longest wavelength for the photoelectric effect?
lambda-0 = hc/phi. Shortcut: lambda-0 (nm) = 1240 / phi (eV). This comes from equating photon energy hc/lambda to the work function phi.
Why does light of wavelength longer than lambda-0 not eject electrons?
Because photon energy E = hc/lambda decreases as wavelength increases. For lambda greater than lambda-0, each photon carries less than phi, so it cannot free an electron even if the light is very bright.
Is the longest wavelength the same as the threshold wavelength?
Yes. 'Longest wavelength that causes photoemission' and 'threshold wavelength' mean exactly the same thing: the wavelength whose photon energy just equals the work function.
How is threshold wavelength related to threshold frequency?
They are linked by lambda-0 = c/nu-0, and both satisfy phi = h.nu-0 = hc/lambda-0. Minimum frequency nu-0 corresponds to maximum wavelength lambda-0.
A metal has work function 2.0 eV. What is its longest usable wavelength?
lambda-0 = 1240/2.0 = 620 nm. Light up to 620 nm (into the orange-red region) can cause emission; longer wavelengths cannot.
