Error Propagation Question - Estimating a value based on straight fit lines

• JesseCoffey
In summary, you correctly used the method of least squares and error propagation to estimate the stopping potential and work function in your experiment on the photoelectric effect.
JesseCoffey
I have already turned this lab report in, but I am sure this will come up in the future. I just want to insure that I am doing it correctly.

Homework Statement

We did an experiment on the photoelectric effect. We found the negative voltage plateau and took readings of the photocurrent for small changes in the voltage being applied.

Homework Equations

Method of Least Squares
Error Propagation

The Attempt at a Solution

The instructor told me that even though the data will show a curve, that we should estimate where the peak is by extending the linear portions of the curve.

What I did was I separated the data into two different groups. Each one of the linear relations. I disregarded the data points on the curve portion that was between the two linear groups.

From these two groups I used the method of least squares to approximate a straight fit line to both relation ships. Once I had my linear equation ( y=m$$\pm$$$$\sigma$$mX + c$$\pm$$$$\sigma$$c )
I used the weighted method using the error I got from my readings (watched the voltmeter for 15 seconds and recorded the high and low)

I subtracted the two equations to find the value of X that satisfied both equations. This is the value i used to Estimate the stopping potential of the specific wavelength.

I repeated this for 7 different wavelengths.

Now that I had a data comparing frequency and stopping potentials, I graphed them together and formed another straight fit line, again using method of least squares.

I used the slope of this line to estimate the value of Planck's constant and to find the work function.

So, my question is, how exactly do I propagate the error through multiple equations?

I did it just as I did the mathematics. When I did the combination of the two line equations: when i subtracted the equations, I just did normal error propagation for the addition of two errors for both m and c. When I did the division to find the final value of x, I again did the normal propagation. This gave me an error of my estimated value.

I used these errors in the least squares error equations for the stopping potential vs frequency. And my final value had one more propagation to go (by substituting zero in for X).

Did I do this correctly? The part that worries me is that the difference in magnitude on the voltage compared to the photocurrent is quite large. so even though my answers were quite nice (linear relationship) the errors were tiny.

Thanks for any clarification.

Yes, you did the error propagation correctly. Error propagation is a mathematical method of calculating the uncertainty of a measurement based on the individual uncertainties of each component used in the calculation. In this case, you used the errors from the two linear equations to calculate the uncertainty of the combined equation, then used that uncertainty to calculate the stopping potential and work function. The magnitude of the voltage compared to the photocurrent does not affect the error propagation, as long as the errors are properly accounted for.

1. What is error propagation and why is it important in estimating a value based on straight fit lines?

Error propagation is the process of quantifying and propagating uncertainties in measurements or calculations to the final result. In the context of estimating a value based on straight fit lines, it is important because it allows us to account for the uncertainties in our data and provide a more accurate estimate of the value.

2. How is error propagation calculated in the context of estimating a value based on straight fit lines?

In the context of estimating a value based on straight fit lines, error propagation is calculated using the standard error of the slope and the standard error of the intercept. These values are then used to calculate the standard error of the estimated value.

3. Can error propagation be used for any type of data or only for data that fits a straight line?

Error propagation can be used for any type of data, as long as the data can be modeled using a mathematical function. In the case of estimating a value based on straight fit lines, the data is assumed to follow a linear relationship, but other types of data can also be analyzed using error propagation techniques.

4. What are some potential sources of error that can affect the accuracy of the estimated value based on straight fit lines?

There are several potential sources of error that can affect the accuracy of the estimated value based on straight fit lines. These include measurement errors, uncertainties in the data, and assumptions made in the analysis process. It is important to carefully consider these potential sources of error and minimize their impact to obtain a more accurate estimate.

5. How can error propagation help in interpreting the estimated value based on straight fit lines?

Error propagation provides a way to quantify the uncertainties associated with the estimated value based on straight fit lines. This can help in interpreting the estimated value by providing a range of values within which the true value is likely to fall. It also allows for comparison between different estimation methods and helps in determining the reliability of the estimated value.

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