The photoelectric work function of potassium is 2.3 eV. If light that has a wavelength of 190 nm falls on potassium, find (b) the kinetic energy, in electron volts, of the most energetic electrons ejected

Verified step by step guidance

1. Convert the wavelength of the light from nanometers to meters by multiplying by $1 \times 10^{-9}$ m/nm.
2. Use the equation $c = \lambda \nu$ to find the frequency of the light, where $c$ is the speed of light ($3 \times 10^8$ m/s) and $\lambda$ is the wavelength in meters.
3. Calculate the energy of the photons using the equation $E = h \nu$, where $h$ is Planck's constant ($6.626 \times 10^{-34}$ J s) and $\nu$ is the frequency calculated in the previous step. Convert this energy from joules to electron volts by dividing by the charge of an electron ($1.602 \times 10^{-19}$ C).
4. Subtract the work function of potassium from the energy of the photons to find the maximum kinetic energy of the ejected electrons. The work function is given as 2.3 eV.
5. The result from the previous step is the kinetic energy of the most energetic ejected electrons, expressed in electron volts.

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, transferring energy. If the energy of the incoming photons exceeds the work function of the material, electrons are ejected with kinetic energy proportional to the excess 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, measured in electron volts (eV). In this case, potassium has a work function of 2.3 eV, meaning that photons must provide at least this amount of energy to eject electrons from its surface.

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 light with a wavelength of 190 nm, we can calculate the energy of the photons striking the potassium surface. If this energy exceeds the work function, the excess energy translates into the kinetic energy of the emitted electrons.