The photoelectric work function of potassium is $2.3$ eV. If light that has a wavelength of $190$ nm falls on potassium, find the stopping potential in volts.

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 stopping potential is the potential needed to stop these ejected electrons.
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 of the photons from joules to electron volts (eV) using the conversion factor \( 1 \, \text{eV} = 1.602 \, imes 10^{-19} \, \text{J} \).
4. Determine the kinetic energy of the ejected electrons using the equation: \( KE = E_{photon} - \text{work function} \). The work function of potassium is given as 2.3 eV.
5. The stopping potential \( V_s \) is equal to the kinetic energy of the ejected electrons divided by the charge of an electron. Use the formula: \( V_s = \frac{KE}{e} \), where \( e \) is the elementary charge \( (1.602 \times 10^{-19} \text{ C}) \).

Key Concepts

Photoelectric Effect

The photoelectric effect occurs when light shines on a material and ejects electrons from its surface. The energy of the incoming photons must be greater than the material's work function to release electrons. This phenomenon is crucial for understanding how light can cause electron emission and is foundational in quantum physics.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material. It is specific to each material and is measured in electron volts (eV). In the context of the photoelectric effect, the work function determines the threshold frequency or wavelength of light needed to eject electrons.

Stopping Potential

Stopping potential is the voltage required to stop the most energetic photoelectrons emitted from a material due to the photoelectric effect. It is calculated using the energy difference between the incoming photons and the work function. The stopping potential provides insight into the kinetic energy of the emitted electrons.