Stopping-Potential Graphs
Combining Einstein's equation with K_max = e V_s gives V_s = (h/e) nu - phi/e. The frequency-axis intercept is the threshold frequency, while parallel lines represent materials measured with the same fundamental constants.
Why this shows up in the exam
Measuring Planck's constant · Comparing work functions of metals · Reading threshold frequency from experimental graphs
Learn the idea
The stopping-potential versus frequency graph is linear, with slope h/e and a material-dependent intercept. Each increase in photon frequency adds the same extra energy per unit frequency. Dividing that energy by electron charge turns the straight kinetic-energy relation into a straight stopping-potential graph.
🧠 Memory hook: Same slope h/e; the material shifts the threshold.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- V_s = (h/e) nu - phi/e — linear stopping-potential relation for a fixed material
- slope = h/e; nu-intercept = phi/h — physical meaning of graph slope and threshold intercept
How to approach it
- 1Write the graph equation before reading slope or intercept
- 2Use the frequency-axis crossing for threshold frequency
- 3Compare horizontal shifts to compare work functions
Common slip-ups that cost marks
- •Taking graph slope as h instead of h/e
- •Treating intensity as a cause of graph slope change
- •Confusing the voltage-axis intercept with threshold frequency
🌟 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.