# 29.2 The photoelectric effect  (Page 4/8)

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## Phet explorations: photoelectric effect

See how light knocks electrons off a metal target, and recreate the experiment that spawned the field of quantum mechanics.

## Test prep for ap courses

A metal exposed to a beam of light with a wavelength equal to or shorter than a specific wavelength emits electrons. What property of light, as described in the quantum explanation of blackbody radiation, accounts for this photoelectric process?

1. The energy of light increases as its speed increases.
2. The energy of light increases as its intensity increases.
3. The energy of light increases as its frequency increases.
4. The energy of light increases as its wavelength increases.

(c)

During his experiments that confirmed the existence of electromagnetic waves, Heinrich Hertz used a spark across a gap between two electrodes to provide the rapidly changing electric current that produced electromagnetic waves. He noticed, however, that production of the spark required a lower voltage in a well-lighted laboratory than when the room was dark. Describe how this curious event can be explained in terms of the quantum interpretation of the photoelectric effect.

## Section summary

• The photoelectric effect is the process in which EM radiation ejects electrons from a material.
• Einstein proposed photons to be quanta of EM radiation having energy $E=\text{hf}$ , where $f$ is the frequency of the radiation.
• All EM radiation is composed of photons. As Einstein explained, all characteristics of the photoelectric effect are due to the interaction of individual photons with individual electrons.
• The maximum kinetic energy ${\text{KE}}_{e}$ of ejected electrons (photoelectrons) is given by ${\text{KE}}_{e}=\text{hf}\text{– BE}$ , where $\text{hf}$ is the photon energy and BE is the binding energy (or work function) of the electron to the particular material.

## Conceptual questions

Is visible light the only type of EM radiation that can cause the photoelectric effect?

Which aspects of the photoelectric effect cannot be explained without photons? Which can be explained without photons? Are the latter inconsistent with the existence of photons?

Is the photoelectric effect a direct consequence of the wave character of EM radiation or of the particle character of EM radiation? Explain briefly.

Insulators (nonmetals) have a higher BE than metals, and it is more difficult for photons to eject electrons from insulators. Discuss how this relates to the free charges in metals that make them good conductors.

If you pick up and shake a piece of metal that has electrons in it free to move as a current, no electrons fall out. Yet if you heat the metal, electrons can be boiled off. Explain both of these facts as they relate to the amount and distribution of energy involved with shaking the object as compared with heating it.

## Problems&Exercises

What is the longest-wavelength EM radiation that can eject a photoelectron from silver, given that the binding energy is 4.73 eV? Is this in the visible range?

263 nm

Find the longest-wavelength photon that can eject an electron from potassium, given that the binding energy is 2.24 eV. Is this visible EM radiation?

What is the binding energy in eV of electrons in magnesium, if the longest-wavelength photon that can eject electrons is 337 nm?

3.69 eV

Calculate the binding energy in eV of electrons in aluminum, if the longest-wavelength photon that can eject them is 304 nm.

What is the maximum kinetic energy in eV of electrons ejected from sodium metal by 450-nm EM radiation, given that the binding energy is 2.28 eV?

0.483 eV

UV radiation having a wavelength of 120 nm falls on gold metal, to which electrons are bound by 4.82 eV. What is the maximum kinetic energy of the ejected photoelectrons?

Violet light of wavelength 400 nm ejects electrons with a maximum kinetic energy of 0.860 eV from sodium metal. What is the binding energy of electrons to sodium metal?

2.25 eV

UV radiation having a 300-nm wavelength falls on uranium metal, ejecting 0.500-eV electrons. What is the binding energy of electrons to uranium metal?

What is the wavelength of EM radiation that ejects 2.00-eV electrons from calcium metal, given that the binding energy is 2.71 eV? What type of EM radiation is this?

(a) 264 nm

(b) Ultraviolet

Find the wavelength of photons that eject 0.100-eV electrons from potassium, given that the binding energy is 2.24 eV. Are these photons visible?

What is the maximum velocity of electrons ejected from a material by 80-nm photons, if they are bound to the material by 4.73 eV?

$1.95×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{m/s}$

Photoelectrons from a material with a binding energy of 2.71 eV are ejected by 420-nm photons. Once ejected, how long does it take these electrons to travel 2.50 cm to a detection device?

A laser with a power output of 2.00 mW at a wavelength of 400 nm is projected onto calcium metal. (a) How many electrons per second are ejected? (b) What power is carried away by the electrons, given that the binding energy is 2.71 eV?

(a) $4.02×{\text{10}}^{\text{15}}\phantom{\rule{0.25em}{0ex}}\text{/s}$

(b) 0.256 mW

(a) Calculate the number of photoelectrons per second ejected from a 1.00-mm 2 area of sodium metal by 500-nm EM radiation having an intensity of $1\text{.}{\text{30 kW/m}}^{2}$ (the intensity of sunlight above the Earth’s atmosphere). (b) Given that the binding energy is 2.28 eV, what power is carried away by the electrons? (c) The electrons carry away less power than brought in by the photons. Where does the other power go? How can it be recovered?

Unreasonable Results

Red light having a wavelength of 700 nm is projected onto magnesium metal to which electrons are bound by 3.68 eV. (a) Use ${\text{KE}}_{e}=\text{hf}–\text{BE}$ to calculate the kinetic energy of the ejected electrons. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

(a) $–1.90 eV$

(b) Negative kinetic energy

(c) That the electrons would be knocked free.

Unreasonable Results

(a) What is the binding energy of electrons to a material from which 4.00-eV electrons are ejected by 400-nm EM radiation? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

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