Figure 27.21 shows a graph of stopping potential versus...

Figure 27.21 shows a graph of stopping potential versus frequency for a photoelectric material. Determine
(a) Planck's constant and (b) the work function of the material from the data contained in the graph.

Key Concepts

Photoelectric Effect

The photoelectric effect is the phenomenon in which electrons are emitted from a material when it is exposed to electromagnetic radiation (light). This process provided crucial evidence for the quantum nature of light, where the energy of photons is quantized and sufficient energy can cause electrons to be ejected from the surface of the material.

Planck's Constant

Planck's constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It is a central quantity in the photoelectric effect, as it appears in the linear relationship between the stopping potential and the frequency of the incident light, where the slope of the line is proportional to Planck’s constant divided by the electron charge.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material. It represents the energy barrier that must be overcome for an electron to escape the material and appears as the intercept (when properly interpreted) in the graph of stopping potential versus frequency in the photoelectric effect.

Stopping Potential

In the context of the photoelectric effect, the stopping potential is the voltage needed to reduce the kinetic energy of the emitted electrons to zero. It is directly related to the maximum kinetic energy of the electrons, serving as a key experimental parameter that, when plotted against frequency, reveals information about Planck's constant and the work function.

Linear Relationship in the Photoelectric Effect

The photoelectric equation shows that the maximum kinetic energy of ejected electrons is equal to the energy of the incident photon minus the work function of the material. Plotting the stopping potential (proportional to kinetic energy) versus the frequency of light yields a straight line whose slope is equal to Planck's constant divided by the electron charge, and whose intercept relates to the work function. This linear relationship is fundamental for experimentally determining both Planck's constant and the work function.

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