Work Function and Threshold
The work function phi is the minimum energy required to remove an electron from a material surface. At threshold the emitted electron has zero maximum kinetic energy, giving phi = h nu_0 = h c / lambda_0.
Why this shows up in the exam
Selecting photocathode materials · Finding threshold wavelength or frequency · Checking whether visible light can eject electrons
Learn the idea
The work function fixes the minimum photon frequency and maximum threshold wavelength for emission. Different metals hold electrons with different strengths. The work function is the least energy needed to free an electron, so it creates a sharp frequency threshold for incident light.
🧠 Memory hook: Threshold frequency is minimum; threshold wavelength is maximum.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- phi = h nu₀ = h c / lambda₀ — relation among work function, threshold frequency, and threshold wavelength
- lambda <= lambda₀ — wavelength condition for photoemission from that surface
How to approach it
- 1Convert the work function into the same energy unit as h nu
- 2Compute nu₀ or lambda₀ at zero kinetic energy
- 3Compare incident frequency upward or wavelength downward with threshold
Common slip-ups that cost marks
- •Calling threshold wavelength the minimum allowed wavelength
- •Using ordinary frequency where angular frequency is intended
- •Forgetting that work function depends on the surface material
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
Photons of energy 5 eV illuminate a metal of work function 2 eV. Find the stopping potential.
More from Dual Nature of Matter and Radiation
Photoelectric Effect
The photoelectric effect describes the emission of electrons from a material when it is exposed to light of sufficient frequency, governed by concepts such as threshold frequency, work function, stopping potential, and the Einstein photoelectric equation.
de Broglie Wavelength and Matter Waves
All matter exhibits wave-like properties, with the de Broglie wavelength inversely proportional to momentum and dependent on factors like velocity, temperature, and particle type.
Photon Properties and Energy-Momentum Relations
Photons are massless particles of light characterized by their energy, frequency, momentum, and charge neutrality, and their interactions obey conservation laws.
Photon Energy and Momentum
For a photon in vacuum, energy is proportional to frequency and momentum is energy divided by c. Frequency and wavelength obey c = nu lambda, so shorter-wavelength photons have larger energy and momentum.
Photon Rate, Power, and Energy Density
For monochromatic radiation, total energy is the number of photons times h nu. Power is energy per unit time, so the photon emission rate equals power divided by single-photon energy.
Radiation Pressure and Photon Momentum Transfer
Radiation force is the rate of photon momentum transfer. For normal incidence on an ideal absorber the pressure is intensity divided by c; for an ideal reflector it is twice that value.