Photoelectric effect
Light knocks electrons out of a metal one photon at a time. Each photon's energy depends only on its frequency, so below a threshold nothing comes out, however bright the light.
Maximum kinetic energy against frequency
读数
发生了什么
Light arrives in packets, photons, each carrying energy E = hf = hc/λ. An electron in the metal can absorb exactly one photon, and it must spend at least the work function φ to escape the surface. Whatever is left over becomes kinetic energy, so the fastest electrons have KEmax = hf − φ (others lose a little more on the way out).
If hf is less than φ, no electron ever escapes, so there is a threshold frequency f₀ = φ/h and a matching threshold wavelength. Turning up the intensity sends more photons per second, which frees more electrons and raises the current, but it does not make any single electron faster. Make the collector negative and it pushes electrons back: the current falls, and it reaches zero when eV equals KEmax, the stopping potential.
Plot KEmax against f and every metal gives a straight line of gradient h, crossing the f-axis at f₀ and meeting the energy axis at −φ. That graph was Millikan's check of Einstein's equation, and the first precise measurement of h from it.
- Photon energyE = hf = hc / λ
- Einstein's photoelectric equationhf = φ + KEmax
- Stopping potentialeVₛ = KEmax
- Threshold frequencyf₀ = φ / h
考试大纲
- A-Level Physics AQA, OCR A and B, Edexcel, WJECthe photoelectric effect, photon energy E = hf, work function, threshold frequency, stopping potential and the electronvolt
挑战
Predict first: sodium (φ = 2.28 eV) is lit with violet light of wavelength 400 nm. What stopping potential just brings the current to zero? Work out hf in electronvolts first, then type your answer and drag the collector voltage to check.
hf = hc/λ = 1240 eV nm / 400 nm = 3.10 eV, so KEmax = 3.10 − 2.28 = 0.82 eV and the stopping potential is 0.82 V. At a collector voltage of −0.82 V the current reaches zero.
系统地学
GCSE Combined and Separate Science 中讲这个主题的课：先看分步讲解，再做考试风格的题目，每次数字都不同。 课程为英文。
常见问题
Why does bright red light not release electrons from zinc?
Each electron absorbs one photon. A red photon has about 1.9 eV, less than zinc's work function of 4.33 eV, so no single photon can free an electron. A brighter beam just sends more of these too-weak photons, and an electron cannot save up energy from several of them.
What is the stopping potential?
It is the smallest reverse voltage on the collector that stops even the fastest photoelectrons, so the current falls to zero. At that point the work done against the field equals the maximum kinetic energy: eVₛ = KEmax = hf − φ.
How do you find Planck's constant from the photoelectric effect?
Measure the stopping potential at several frequencies and plot eVₛ (or KEmax) against f. The points lie on a straight line whose gradient is h and whose intercept on the energy axis is −φ.
Does intensity change the kinetic energy of the electrons?
No. Intensity sets how many photons arrive per second, so it changes the current. The energy of each photon, and so KEmax and the stopping potential, depends only on the frequency.
How do I find the work function from a stopping potential?
Use φ = hf − eVₛ. Light of 250 nm carries hf = 1239.8/250 = 4.96 eV; if the stopping potential is 0.63 V, φ = 4.96 − 0.63 = 4.33 eV, which is zinc. φ from Vₛ in the Solve for panel does it with the working.