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Chapter 27: Problem 60

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). $$\begin{array}{lcc} \hline \text { Color } & \text { Wavelength (nm) } & \text { Stopping Potential (V) } \\\ \text { Yellow } & 578 & 0.40 \\\ \text { Green } & 546 & 0.60 \\\ \text { Blue } & 436 & 1.10 \\\ \text { Ultraviolet } & 366 & 1.60 \\\ \hline \end{array}$$

Short Answer

Expert verified
In conclusion, to analyze the data on stopping potential and wavelengths of light for the photoelectric effect, we would create a graph of stopping potential versus the reciprocal of the wavelength and find the values of work function, threshold wavelength, and the slope of the graph. Then, we would compare the slope of the graph with the expected value calculated using fundamental constants. This process would help us determine if the photoelectric effect is behaving according to the expected theoretical relationship.

Step by step solution

01

Convert wavelengths to their reciprocals

First, convert the given wavelengths to their reciprocals (in units of nm^-1) by taking the inverse of each wavelength.
02

Create a table with the new values

Next, create a new table containing the stopping potentials and reciprocal wavelengths: Color | Reciprocal Wavelength (nm^-1) | Stopping Potential (V) --- | --- | --- Yellow | 0.001731 | 0.40 Green | 0.001831 | 0.60 Blue | 0.002294 | 1.10 Ultraviolet | 0.002732 | 1.60
03

Plot the graph

Use the table created in step 2, plot a graph with reciprocal wavelengths on the x-axis and stopping potential on the y-axis.
04

Determine the work function and threshold wavelength from the graph

With the help of the graph, find the point at which the line intersects the x-axis (where stopping potential is equal to zero). The corresponding wavelength at this point is the threshold wavelength. To find the work function, use the y-intercept of the line, but be sure to convert it to eV (electron-Volt) using the conversion factor of 1 eV = 1.602 x 10^-19 J, if needed.
05

Find the slope of the graph

To find the slope of the graph, use any two points from the table in Step 2 and calculate the change in stopping potential (y) divided by the change in reciprocal wavelength (x). For example, using the Yellow and Green data points: Slope = (0.60 - 0.40) / (0.001831 - 0.001731) = 2.00 V nm^-1
06

Compare the slope with the expected value

To compare the slope with the expected value, we need to use the relation between the stopping potential and the wavelength, as described by the Einstein's photoelectric equation: $$V = \frac{h}{e}\left(\frac{1}{\lambda} - \frac{1}{\lambda_0}\right)$$ Where \(V\) is the stopping potential, \(h\) is Planck's constant, \(e\) is the charge of an electron, \(\lambda\) is the wavelength, and \(\lambda_0\) is the threshold wavelength. The constant term \(\frac{h}{e}\) is called the Planck's constant in eV and has a value of about 4.14 x 10^-15 eV.s. Using this equation, we can determine the expected slope (in V.nm) from the Planck's constant: $$slope=\frac{h}{e}$$ By calculating the expected value, we can compare it with the obtained value from the graph. If the values are close, it will confirm that the photoelectric effect is behaving according to the expected theoretical relationship.

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Most popular questions from this chapter

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