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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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.

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.