Question:

In an experiment to investigate the photoelectric effect, a metal surface is illuminated with light of different frequencies. The stopping potential for the photoelectrons is measured as a function of frequency and the results are shown in the graph below.

1. Determine the value of Planck's constant, h, using the data from the graph.
2. Explain, using the concept of the photoelectric effect, why there is no photoelectric emission for frequencies below a certain threshold.

Answer:

1. To determine the value of Planck's constant, h, we can use the equation for the photoelectric effect:

Where:

• $E_{\text{photon}}$ is the energy of the incident photon
• $h$ is Planck's constant
• $f$ is the frequency of the incident light
• Work function is the minimum energy required to remove an electron from the surface of the metal

From the graph, we can see that the stopping potential (V) is related to the frequency (f) by the equation:

Where:

• $e$ is the elementary charge
• $V$ is the stopping potential
• $\phi$ is the work function

Solving for the slope of the graph gives:

Using the data from the graph, we can pick two data points and find the slope:

$\Delta(eV) = 2.0\,V - 0\,V = 2.0\,V$

$\Delta f = 6.0\times10^{14}Hz - 4.0\times10^{14}Hz = 2.0\times10^{14}Hz$

Therefore, the value of Planck's constant, $h$, is $1.0\times10^{-34}\,J\cdot s$.

2. Photoelectric emission occurs when the energy of the incident photons (hf) is greater than the work function ($\phi$) of the metal. Below a certain threshold frequency, the energy of the incident photons is not sufficient to overcome the work function and eject electrons from the metal. This is because the energy of a photon is directly proportional to its frequency, and only photons with sufficient energy (i.e., frequency) can eject electrons from the metal surface. Hence, no photoelectric emission occurs for frequencies below the threshold.

This phenomenon is a demonstration of the particle-like nature of light (photons) and is a key aspect of the photoelectric effect as explained by Albert Einstein.