Einstein Photoelectric Equation
Energy conservation for one-photon photoemission gives h nu = phi + K_max. The stopping potential is the reverse potential whose electric potential energy e V_s equals K_max.
Why this shows up in the exam
Finding photoelectron kinetic energy · Determining stopping potential · Comparing two incident wavelengths on one metal
Learn the idea
A photon spends the work function first, and the remainder becomes electron kinetic energy. Treat photon energy like a fixed budget. The metal requires an entry cost called the work function; only the energy left after paying that cost can appear as the fastest electron's kinetic energy.
🧠 Memory hook: Photon budget equals escape cost plus maximum kinetic energy.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- h nu = phi + K_max — Einstein photoelectric equation for the fastest emitted electrons
- K_max = e V_s = (1/2) m_e v_max² — equivalent forms of maximum photoelectron kinetic energy
How to approach it
- 1Write h c / lambda = phi + K_max
- 2Replace K_max by e V_s or one-half m v squared as needed
- 3Subtract two equations when the same metal is used twice
Common slip-ups that cost marks
- •Using incident intensity in the energy equation
- •Writing e V_s equal to photon energy without subtracting work function
- •Mixing electron-volts and joules within one calculation
🌟 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.