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

Verified step by step guidance

1. First, understand the concept of the photoelectric effect. When light falls on a material, it can eject electrons if the energy of the photons is greater than the work function of the material. The work function is the minimum energy needed to eject an electron from the surface of the material.
2. Calculate the energy of the incoming photons using the formula: \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant \( (6.626 \times 10^{-34} \text{ Js}) \), \( c \) is the speed of light \( (3 \times 10^8 \text{ m/s}) \), and \( \lambda \) is the wavelength of the light \( (190 \text{ nm} = 190 \times 10^{-9} \text{ m}) \).
3. Convert the energy calculated in step 2 from joules to electron volts. Recall that 1 eV = \( 1.602 \times 10^{-19} \text{ J} \).
4. Determine the kinetic energy of the ejected electrons using the equation: \( KE = E_{photon} - \phi \), where \( E_{photon} \) is the energy of the incoming photons and \( \phi \) is the work function of potassium (2.3 eV).
5. Interpret the result: The kinetic energy calculated in step 4 represents the maximum kinetic energy of the electrons ejected from the potassium surface when exposed to light of 190 nm wavelength.

Key Concepts

Photoelectric Effect

The photoelectric effect occurs when light shines on a material, causing it to emit electrons. The energy of the incoming photons must be greater than the material's work function to eject electrons. The excess energy is converted into the kinetic energy of the emitted electrons.

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 the material and is measured in electron volts (eV). For potassium, the work function is 2.3 eV, which must be overcome by the energy of the incident photons.

Photon Energy Calculation

Photon energy can be calculated using the formula E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of the light. For a wavelength of 190 nm, this formula helps determine the energy of the photons, which is crucial for calculating the kinetic energy of ejected electrons.