What would the minimum work function for a metal have to be for visible light (380–750 nm) to eject photoelectrons?

Verified step by step guidance

1. Identify the range of wavelengths for visible light, which is from 380 nm to 750 nm. The minimum wavelength (380 nm) will be used to find the maximum energy of the photons, as energy is inversely proportional to wavelength.
2. Convert the wavelength from nanometers to meters by multiplying by $10^{-9}$, so 380 nm becomes $380 \times 10^{-9}$ meters.
3. Use the formula for the energy of a photon, $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant ($6.626 \times 10^{-34}$ Js), $c$ is the speed of light ($3.00 \times 10^8$ m/s), and $\lambda$ is the wavelength of the light.
4. Calculate the energy of the photon using the converted wavelength. This energy represents the maximum energy that photons of visible light can have.
5. The minimum work function of the metal, $\phi$, must be less than or equal to this photon energy for photoelectrons to be ejected. Therefore, the minimum work function for the metal to eject photoelectrons with visible light is the energy calculated in the previous step.

Key Concepts

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material. It is a critical parameter in photoelectric effect experiments, as it determines the threshold frequency of light needed to eject electrons. The work function is typically measured in electron volts (eV) and varies among different materials.

Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are emitted from a material when it absorbs light of sufficient energy. This effect demonstrates the particle nature of light, where photons collide with electrons, transferring energy. If the energy of the incoming photons exceeds the work function of the material, electrons are ejected.

Photon Energy and Wavelength

The energy of a photon is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. For visible light, which ranges from 380 to 750 nm, the corresponding photon energies can be calculated. To eject photoelectrons, the photon energy must be greater than or equal to the work function of the metal.