These data are obtained for photoelectric stopping...

These data are obtained for photoelectric stopping potentials using light of four different wavelengths. (a) Plot a graph of the stopping potential versus the reciprocal of the wavelength. (b) Read the values of the work function and threshold wavelength for the metal used directly from the graph. (c) What is the slope of the graph? Compare the slope with the expected value (calculated from fundamental constants). $$\begin{array}{lcc} \hline \text { Color } & \text { Wavelength (nm) } & \text { Stopping Potential (V) } \\ \text { Yellow } & 578 & 0.40 \\ \text { Green } & 546 & 0.60 \\ \text { Blue } & 436 & 1.10 \\ \text { Ultraviolet } & 366 & 1.60 \\ \hline \end{array}$$

These data are obtained for photoelectric stopping potentials using light of four different wavelengths.
(a) Plot a graph of the stopping potential versus the reciprocal of the wavelength. (b) Read the values of the work function and threshold wavelength for the metal used directly from the graph. (c) What is the slope of the graph? Compare the slope with the expected value (calculated from fundamental constants). $$\begin{array}{lcc} \hline \text { Color } & \text { Wavelength (nm) } & \text { Stopping Potential (V) } \\ \text { Yellow } & 578 & 0.40 \\ \text { Green } & 546 & 0.60 \\ \text { Blue } & 436 & 1.10 \\ \text { Ultraviolet } & 366 & 1.60 \\ \hline \end{array}$$

Key Concepts

Photoelectric Effect

This phenomenon describes the emission of electrons from a material when it is exposed to light of sufficiently high frequency. Einstein’s explanation of the photoelectric effect introduced the idea that light consists of discrete packets of energy (photons), where the energy of each photon is proportional to its frequency. The effect established a direct relationship between the energy of incident light and the kinetic energy of emitted electrons, emphasizing the role of the work function of the material.

Stopping Potential

The stopping potential is the minimum voltage needed to stop the most energetic photoelectrons from reaching the anode. It is directly related to the maximum kinetic energy of the emitted electrons, allowing one to determine the energy imparted by the photons when the work function is subtracted from the total photon energy. The stopping potential therefore forms a critical measurement in experiments exploring the photoelectric effect.

Work Function

The work function is the minimum energy required to eject an electron from the surface of a material. It represents an intrinsic property of the metal and acts as an energy barrier in the photoelectric effect. Experimentally, it can be deduced from the intercept on the stopping potential graph, providing insight into the binding energy of electrons in the material.

Threshold Wavelength

The threshold wavelength is the longest wavelength (or equivalently, the lowest frequency) that can still eject electrons from a given material. Beyond this wavelength, the photon energy falls below the work function and no photoelectrons are emitted. It provides a critical value for understanding the limits of the photoelectric effect and the material’s response to electromagnetic radiation.

Graph Analysis and Slope

Plotting the stopping potential versus the reciprocal of the wavelength should produce a straight line according to the linear form of the photoelectric equation, with the slope representing the product of Planck's constant and the speed of light. Analyzing the slope allows for comparison with the theoretical prediction derived from these fundamental constants, thereby confirming the quantum description of light.

Transcript

00:01 In this exercise, we have a table with data from a photoelectric experiment.

00:06 So we have here the stopping potential v in volts as a function of the wavelength of the incoming light, lambda.

00:17 And in the first exercise, in the first question, a, we have to draw a plot of this data, of the stopping potential as a function of the inverse of the wavelength.

00:33 So the first thing we need to do is you calculate the inverse of the wavelength.

00:37 So for 578 nanometers, the inverse is going to be 1 .73.

00:43 And this is already in 10 to the 6 meters to the minus 1.

00:49 Then we're going to have 1 .83, 2 .29, and 2 .73.

00:58 And now we are in our position to draw the plot, so i'm going to draw it.

01:05 Now in order to save some time, i went ahead and draw the plot and i'm showing it to you.

01:12 So here in the y -axis we have the stopping potential.

01:16 In the x -axis, we have lambda to the minus 1 in units of 10 to the 6 meters to the minus 1.

01:25 And i'm going to go ahead and try to draw a line fitting this.

01:30 Is plot.

01:33 Okay, so it's here.

01:34 It's the best it can do.

01:36 And in question b, we are asked to calculate, or better, not only to calculate, we are asked to look at the graph and extract directly, look at the plots, i'm sorry, and extract directly from it, the values of the work function and the cutoff frequency for this material.

02:01 So you can do it.

02:04 The work function is going to be the minus the intercept of the graph, of the plot.

02:10 And that's because the photoelectric formula is ev equals to hc, lambda to the minus 1 minus phi.

02:26 So that v is going to be hc over e, lambda to the minus 1, minus 5.

02:33 Over e so phi over e is going to be minus the intercept okay so minus the intercept is around here right so around 1 .5 somewhere around 1 .5 electron volts sorry so that phi is somewhere around 1 .5 electron volts.

02:54 Sorry so that phi is somewhere around 1 .5 electron volts.

03:02 Okay that's the approximate work function.

03:06 We can also draw the value of the cutoff wavelength.

03:12 That's when the wavelength for which the the value of the stopping potential is zero.

03:18 So it's here around 1 .3 times 10 to 6 meters to the minus 1.

03:28 So you can calculate the cutoff potential, the cutoff wavelength as 1 over 1 .3 times cent to the minus to the 6th, i'm sorry...

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