Photoelectrons and Planck's constant

AI Thread Summary
The discussion revolves around calculating Planck's constant using a linear graph of photoelectrons, where the user struggles with finding the slope and y-intercept due to limited data points. It is suggested that extrapolating the line can help determine the y-intercept, which is essential for calculating the work function and ultimately Planck's constant. The importance of algebra in determining the slope from two points on the line is emphasized, as well as the need to convert energy units from eV to joules for accurate results. The conversation highlights that empirical measurements rarely yield exact values, but close approximations can be achieved. Overall, the participants encourage using available data effectively to derive meaningful scientific insights.
benca
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Homework Statement
Use the graph to determine Planck's constant.
Relevant Equations
E = hf
Ek = hf - W

h = Planck's constant
f = frequency
W = work function
Attempt:

I was thinking of finding the slope of the graph but I only know the values for x = 10, y = 3 and y = 0. And without the y-intercept, I don't know the work function and can't solve for h. If you can't see from the picture, the last co-ordinate is (10,3) and the x-axis is measured in f x 10^14 Hz

I'm not sure what options I have left if I don't know how to figure out the slope or work function.

20191123_181808.jpg
 
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The graph is of a straight line. Could you not simply extrapolate the line to find the y-intercept?

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I thought of that too, but I wouldn't exactly get Planck's constant but instead a number close to Planck's constant. But if that's what I need to do then that's ok, thanks
 
benca said:
I thought of that too, but I wouldn't exactly get Planck's constant but instead a number close to Planck's constant. But if that's what I need to do then that's ok, thanks
Yup. You need to squeeze what you can from the given data. That's a truism for experimental science, where you collect measured data over a limited region and suggest reasonable extrapolations to complete the overall picture for purposes of analysis. In this case the graph is clearly linear, so a linear extrapolation would not be an unreasonable proposition.
 
gneill said:
Yup. You need to squeeze what you can from the given data. That's a truism for experimental science, where you collect measured data over a limited region and suggest reasonable extrapolations to complete the overall picture for purposes of analysis. In this case the graph is clearly linear, so a linear extrapolation would not be an unreasonable proposition.

Alright, thanks
 
benca said:
Alright, thanks
Happy to be of help! Cheers!
 
The straight line has the form ## y=mx+b ##. In this case ## y=E_k ## and ## x=f ##. The slope is found as Planck's constant ## h=m=\frac{y_2-y_1}{x_2-x_1} ##. From what I could see, you apparently need a brush up on your algebra. Here ## (x_1,y_1) ## and ## (x_2,y_2) ## are any two points on the straight line. ## \\ ## In addition, once you have ## m ##, you can then write ##m=\frac{y-y_1}{x-x_1} ##, and ultimately solve for ##b=-W ##, which is the y-intercept. This problem is a simple one, but you need to be able to do algebra.
 
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benca said:
I thought of that too, but I wouldn't exactly get Planck's constant but instead a number close to Planck's constant. But if that's what I need to do then that's ok, thanks
You never get an exact value from measurements. That is the nature of empirical sciences.

Also, to spell out what others have noted: You only need two points on a line to determine its coefficients. Three will give you an overconstrained system and with measurement errors present you will typically need something like a least squares method to determine the best fitting line.
 
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On this one, if you pick ##(10,3) ## and ##(2.75,0) ## as your two points, you do get close to two decimal place accuracy. ## \\ ## One thing that should be mentioned is that energy is in eV here, and you need to convert to joules to get a number that is approximately the accepted value of Planck's constant ##h=6.626 E-34 ## joule-sec. Otherwise, you get the number in eV-seconds. I would venture to guess that most physics people know this number as 6.626E-34 joule-sec, but don't know its value in units of eV-seconds.
 
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  • #10
Charles Link said:
I would venture to guess that most physics people know this number as 6.626E-34 joule-sec
Most physicists I know (admittedly mainly particle phycisists) know the number as ##2\pi## due to preferring natural units.
 
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  • #11
Orodruin said:
Most physicists I know (admittedly mainly particle phycisists) know the number as ##2\pi## due to preferring natural units.
That is a much more advanced version, where ## \hbar=c=1 ##, but here we are at the Physics 101 level. :smile:
 
  • #12
Charles Link said:
That is a much more advanced version, where ## \hbar=c=1 ##, but here we are at the Physics 101 level. :smile:
In a few weeks I will be giving an ”inspirational” lecture about the geometry of relativity to the same students I taught vector analysis the past spring and went on and on about making sure their physical dimensions always work out ... letting c = 1 should be great fun!
 
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  • #13
Hopefully the OP @benca returns to complete the exercise. If he works it through, I think he will be surprised how close the result he gets is to ## h=6.626E-34 ##. From the data that was supplied, you can't get 3 decimal place accuracy, but you can get pretty close to two decimal places.
 
  • #14
Charles Link said:
That is a much more advanced version, where ## \hbar=c=1 ##, but here we are at the Physics 101 level. :smile:
As you suggested, much too advanced for an introductory physics homework forum.
 
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