Ch 38: Quantization

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo

Knight Calc 5th Edition

Ch 38: Quantization

Problema 3

Capitolo 38, Problema 3

Electrons in a photoelectric-effect experiment emerge from an aluminum surface with a maximum kinetic energy of 1.30 eV. What is the wavelength of the light?

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Understand the photoelectric effect equation: The energy of the incident photon is used to overcome the work function of the material and provide kinetic energy to the ejected electron. The equation is:

E_{photon} = \(\text{Work Function}\) + KE_{max}

Convert the given maximum kinetic energy from electron volts (eV) to joules (J) if needed. Use the conversion factor:

1 \(\text{ eV}\) = 1.602 	imes 10^{-19} \(\text{ J}\)

Determine the work function of aluminum. The work function is the minimum energy required to eject an electron from the surface of the material. For aluminum, it is approximately

4.28 \(\text{ eV}\)

. Convert this value to joules if necessary.

Calculate the energy of the incident photon using the photoelectric equation:

E_{photon} = \(\text{Work Function}\) + KE_{max}

. Ensure all values are in the same unit (joules).

Relate the energy of the photon to its wavelength using the equation:

E_{photon} = rac{hc}{\(\text{wavelength}\)}

, where

h = 6.626 	imes 10^{-34} \(\text{ J·s}\)

is Planck's constant and

c = 3.00 	imes 10^{8} \(\text{ m/s}\)

is the speed of light. Rearrange to solve for the wavelength:

\(\text{wavelength}\) = rac{hc}{E_{photon}}

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Photoelectric Effect

The photoelectric effect is a phenomenon where electrons are emitted from a material when it absorbs light of sufficient energy. This effect demonstrates the particle nature of light, as photons must have a minimum energy threshold to dislodge electrons from the surface of a material, such as aluminum. The maximum kinetic energy of the emitted electrons is determined by the energy of the incoming photons minus the work function of the material.

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Percorso guidato

07:40

The Doppler Effect

Photon Energy

The energy of a photon is directly related to its frequency and inversely related to its wavelength, described by the equation E = hf, where E is energy, h is Planck's constant, and f is frequency. In the context of the photoelectric effect, the energy of the incoming photons must be greater than the work function of the material for electrons to be emitted. The relationship between energy and wavelength is given by E = hc/λ, where c is the speed of light and λ is the wavelength.

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04:10

Intro to Energy & Types of Energy

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material. It is a characteristic property of each material and is crucial in determining the threshold frequency of light needed to initiate the photoelectric effect. If the energy of the incoming photons exceeds the work function, the excess energy is converted into the kinetic energy of the emitted electrons.

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08:30

Intro to Wave Functions

Pratica correlata

Domanda del libro di testo

What is the wavelength, in nm, of a photon with energy (a) 0.30 eV, (b) 3.0 eV, and (c) 30 eV? For each, is this wavelength visible, ultraviolet, or infrared light?

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Domanda del libro di testo

Photoelectrons are observed when a metal is illuminated by light with a wavelength less than 388 nm. What is the metal's work function?

740

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Domanda del libro di testo

A photoelectric-effect experiment finds a stopping potential of 1.56 V when light of 200 nm is used to illuminate the cathode. From what metal is the cathode made?

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