The graph in FIGURE P38.42 was measured in a photoelectric-effect experiment. What is the work function (in eV) of the cathode?

검증된 단계별 안내

Step 1: Understand the photoelectric effect equation, which is given by \( eV_{\text{stop}} = hf - \phi \), where \( V_{\text{stop}} \) is the stopping potential, \( h \) is Planck's constant, \( f \) is the frequency of the incident light, and \( \phi \) is the work function of the material.

Step 2: Analyze the graph provided. The graph shows \( V_{\text{stop}} \) (stopping potential) on the y-axis and \( f \) (frequency) on the x-axis. The linear relationship indicates that \( V_{\text{stop}} \) increases with frequency.

Step 3: Identify the threshold frequency \( f_{\text{threshold}} \) from the graph. This is the frequency at which \( V_{\text{stop}} = 0 \). From the graph, \( f_{\text{threshold}} \) appears to be approximately \( 1 \times 10^{15} \, \text{Hz} \).

Step 4: Use the relationship \( \phi = hf_{\text{threshold}} \) to calculate the work function. Here, \( h \) is Planck's constant, \( h = 6.626 \times 10^{-34} \, \text{J·s} \). Convert \( \phi \) to electron volts (eV) using the conversion factor \( 1 \, \text{eV} = 1.602 \times 10^{-19} \, \text{J} \).

Step 5: Substitute \( f_{\text{threshold}} \) and \( h \) into the equation \( \phi = hf_{\text{threshold}} \) and perform the unit conversion to express the work function in eV. This will give the final value of \( \phi \).

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주요 개념

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Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are emitted from a material, typically a metal, when it is exposed to light of sufficient frequency. This effect demonstrates the particle nature of light, as photons must have enough energy to overcome the work function of the material to release electrons. The relationship between the frequency of incident light and the kinetic energy of emitted electrons is crucial for understanding this effect.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material. It is a critical parameter in the photoelectric effect, as it determines the threshold frequency below which no electrons are emitted, regardless of the intensity of the light. The work function is typically expressed in electronvolts (eV) and can be calculated from the intercept of the graph of stopping potential versus frequency.

Stopping Potential

Stopping potential is the voltage needed to stop the most energetic photoelectrons emitted from a material in a photoelectric experiment. It is directly related to the kinetic energy of the emitted electrons, which can be calculated using the equation KE = eV_stop, where e is the charge of an electron. The stopping potential is plotted against the frequency of the incident light to determine the work function and analyze the photoelectric effect.