White light, λ=400 . to 750 . nm, falls on barium (ϕ=2.48 eV) a) What is the maximum kinetic ene

step 1 White light with a wavelength of 400 to 750 nanometers falls on barium that has a work function

White light, λ=400 . to 750 . nm, falls on barium (ϕ=2.48...

White light, $\lambda=400 .$ to $750 . \mathrm{nm},$ falls on barium $(\phi=2.48 \mathrm{eV})$ a) What is the maximum kinetic energy of electrons ejected from it? b) Would the longest-wavelength light eject electrons? c) What wavelength of light would eject electrons with zero kinetic energy?

White light, $\lambda=400 .$ to $750 . \mathrm{nm},$ falls on barium $(\phi=2.48 \mathrm{eV})$
a) What is the maximum kinetic energy of electrons ejected from it?
b) Would the longest-wavelength light eject electrons?
c) What wavelength of light would eject electrons with zero kinetic energy?

Key Concepts

Threshold Frequency and Cutoff Wavelength

The threshold frequency is the minimum frequency of incident light required to eject electrons from the surface of a material, determined by the work function (?_threshold = ?/h). Correspondingly, the cutoff wavelength is the maximum wavelength that can eject electrons, calculated using ?_cutoff = hc/?. Light with wavelengths longer than this cutoff will not have enough energy to liberate electrons.

Einstein's Photoelectric Equation

Einstein's photoelectric equation relates the maximum kinetic energy of the ejected electrons to the energy of the incident photons and the work function of the metal. The equation is expressed as KE_max = h? - ?, where KE_max is the maximum kinetic energy, h? is the energy of the photon, and ? is the work function.

Work Function

The work function is the minimum amount of energy required to remove an electron from the surface of a material. It is a critical property of metals in the context of the photoelectric effect, as only photons with energy equal to or greater than the work function can cause electron emission.

Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are emitted from a material, typically a metal, when it is exposed to electromagnetic radiation of sufficient energy. The effect supports the quantum nature of light and demonstrates that light comes in quanta, or photons, each carrying an energy proportional to its frequency.

Photon Energy

Photon energy is given by the equation E = h?, where h is Planck's constant and ? is the frequency of the light. Alternatively, using the wavelength, the energy can be expressed as E = hc/?. This relationship helps in determining whether the incoming photon has enough energy to eject an electron from the material's surface.

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