Cesium metal is frequently used in photoelectric cells because the amount of energy necessary to eject electrons from a cesium surface is relatively small—only 206.5 kJ/mol. What wavelength of light in nanometers does this correspond to?

Verified step by step guidance

1. Identify the energy required to eject electrons from the cesium surface, which is given as 206.5 kJ/mol.
2. Convert the energy from kJ/mol to J/photon. Use the conversion factor: 1 kJ = 1000 J and Avogadro's number (6.022 x 10^23 mol^-1) to find the energy per photon.
3. Use the equation E = h\nu, where E is the energy per photon, h is Planck's constant (6.626 x 10^-34 J·s), and \nu is the frequency of the light. Rearrange the equation to solve for \nu: \nu = E/h.
4. Use the relationship between frequency and wavelength: c = \lambda\nu, where c is the speed of light (3.00 x 10^8 m/s) and \lambda is the wavelength. Rearrange to solve for \lambda: \lambda = c/\nu.
5. Convert the wavelength from meters to nanometers by multiplying by 10^9, since 1 meter = 10^9 nanometers.

Key Concepts

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, providing them enough energy to overcome the material's work function, which is the minimum energy required to eject an electron.

Energy and Wavelength Relationship

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. This relationship indicates that shorter wavelengths correspond to higher energy photons, which is crucial for understanding how light can cause electron ejection in the photoelectric effect.

Conversion of Energy Units

In this context, energy is given in kJ/mol, which must be converted to joules per photon for calculations involving individual photons. Since 1 kJ = 1000 J and 1 mol contains Avogadro's number of particles (approximately 6.022 x 10^23), converting kJ/mol to J/photon allows for the application of the energy-wavelength relationship to find the corresponding wavelength of light.