The Particle Nature of Light and the Wave Nature of Electrons
First, violet light with a wavelength of 400 nm shines on sodium. The light intensity is increased, and the number of electrons emitted in 1 second and their maximum kinetic energy are measured.
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光の強さを4倍にすると、電子の最大運動エネルギーは何eVか？
赤い光（650 nm）を4倍に強めると、電子は出るか？
The equations explain the phenomenon
1Light shines on a metal.Kmax∝ν − ν₀……
2Light is modeled as particles.E=h ν……
3Conservation of energy is applied to a single electron.Kmax=h ν−W……
4The threshold wavelength for electron emission is determined.λ₀=h cW……
So far, we have examined energy transfer from photons to electrons. Next, we examine energy transfer from accelerated electrons to X-ray photons and find the minimum wavelength.
5Accelerated electrons strike a metal and produce X-rays.λmin=h ce V……
6The momentum of a photon is determined.p=hλ……
7Conservation equations are written for a collision between a photon and an electron.h cλ+m c²=h cλ′+Ee……
8The electron energy Ee is eliminated.(p − p′)² c²+2 (p − p′) m c³=pe² c²……
9The electron momentum is eliminated to find the wavelength change.λ′ − λ=(hm c)(1 − cosφ)……
10Electrons are proposed to have wave properties.λ=hp……
11Electrons strike a crystal.2 d sinθ=n λ……
12Electrons pass through one at a time.Probability density for the detection position∝|probability amplitude ψ|²……
What this chapter has shown
In the photoelectric effect, light energy is absorbed in units of individual photons. For a given metal and frequency that produces electron emission, increasing the light intensity increases the number of emitted electrons while leaving their maximum kinetic energy unchanged. Electrons are detected individually, but many detection points form interference fringes. The electron wavelength is given by λ=h/p.
0.80 eVKmax remains unchanged even at 4 times the intensity
Under these conditions, even increasing the intensity of red light (650 nm) by a factor of 4 produces no electron emission.
In everyday lifeIn a camera's image sensor, photons absorbed by a semiconductor generate electrons and other charge carriers that can carry electric current. These are read out as an electrical signal.
Detailed summary
The photoelectric effect showed that light consists of particles, each with energy hν. Increasing the intensity of light only increases the number of photons, so the maximum kinetic energy of 1 electron is determined by the frequency. Electron diffraction showed that electrons behave as waves with wavelength h/p. These properties cannot be derived from the equations of motion and must be accepted on the basis of experimental evidence. Nevertheless, conservation of momentum and energy still applies to collisions between photons and electrons. University quantum mechanics begins with the search for an equation that governs the motion of objects that behave as both particles and waves.