The experimental observation of the Photoelectric Effect was one of the key expe

Question

The experimental observation of the Photoelectric Effect was one of the key experiments that demonstrated that photons can behave like particles and aided in establishing the principle of wave-particle duality.

a. Explain in your own words why the experimental observation of the photoelectric effect goes against expectations from classical physics.

b. The energy required to ionize Cs atoms in the gas phase is 3.89 eV. A photon of unknown wavelength is used to ionize a Cs atom, releasing an electron with velocity 1.6 × 105 m/s. What is the wavelength of the photon?

c. Some data is given below indicating how the kinetic energy of electrons ejected from sodium metal via the photoelectric effect depend on the wavelength of the incident radiation. Use the data to calculate both Plank’s constant and the work function of sodium metal.

Wavelength [nm] 100, 200, 300, 400, 500

Kinetic Energy [eV] 10.1, 3.94, 1.88, 0.842, 0.222

d. The ionization potential of an atom of sodium in the gas phase is 5.14 eV which differs from the work function you should find from part (c). Why is this the case?

Explanation / Answer

a) When light shines on the surface of a metallic substance, electrons in the metal absorb the energy of the light and they can escape from the metal's surface. This is called the photoelectric effect, and it is used to produce the electric current that runs many solar-powered devices. Using the idea that light is a wave with the energy distributed evenly throughout the wave, classical physicists expected that when using very dim light, it would take some time for enough light energy to build up to eject an electron from a metallic surface. WRONG!! Experiments show that if light of a certain frequency can eject electrons from a metal, it makes no difference how dim the light is. There is never a time delay.

Albert Einstein came up with the solution. If Max Planck's idea that energy comes in quanta is correct, then light must consist of a stream of clumps of energy. Each clump of light energy is called a photon, said Einstein, and each photon has an energy equal to hf (Planck's constant times the frequency of the light). Therefore the energy of light is not evenly distributed along the wave, but is concentrated in the photons.

A dimmer light means fewer photons, but simply turning down the light (without changing its frequency) does not alter the energy of an individual photon. So for a specific frequency light, if a single photon has enough energy to eject an electron from a metallic surface, then electrons will always be ejected immediately after the light is turned on and the photons hit the metal.

2) v= 1.6 × 10^5 m/s

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