# Use linear regression to find Planck’s constant

• ChiralSuperfields
In summary, the conversation is about using Excel to find Planck's constant using given data on frequency and photon energy. The person asking the question is using linear regression and has set the intercept to zero, but is getting a slightly incorrect value for h. It is suggested that the honest treatment would be to plot frequency vs. photoelectron energy and extract the work function and Planck's constant as the intercept and slope of the regression line. The person responds that they did not collect the data themselves and were taught to set the intercept to zero, but will keep the suggested points in mind.
ChiralSuperfields
Homework Statement
Relevant Equations
E = hf
I am trying to find Planck's constant using Excel given the data:

 Frequency [Hz] Photon Energy [J] 7.5E+14​ 4.90E-19​ 6.7E+14​ 4.50E-19​ 6E+14​ 4.00E-19​ 5.5E+14​ 3.60E-19​ 5E+14​ 3.30E-19​ 4.6E+14​ 3.00E-19​ 4.3E+14​ 2.80E-19​ 4E+14​ 2.65E-19​ 3.75E+14​ 2.50E-19​
I am using Linear regression and I have set the intercept to zero since photon energy is directly proportional to frequency from Planck's Law

My graph is,

However, why is the linear regression giving an incorrect value for h? According to the data Planck's Constant is ##7 \times 10^{-34} Js ## but it meant to be ##6.63 \times 10^{-34} Js##

Many thanks!

Callumnc1 said:
However, why is the linear regression giving an incorrect value for h? According to the data Planck's Constant is ##7 \times 10^{-34} Js ## but it meant to be ##6.63 \times 10^{-34} Js##

Many thanks!
You can tell the spreadsheet software how many sig figs to show in the formula.

ChiralSuperfields
haruspex said:
You can tell the spreadsheet software how many sig figs to show in the formula.

I will try 3 sig figs just like the Planck's constant then.

Many thanks!

Callumnc1 said:

I will try 3 sig figs just like the Planck's constant then.

Many thanks!
Thank you @haruspex!

I have done that and got:

That is probably the most accurate experimental value for h I'm going to get.

Thank you!

Callumnc1 said:
Thank you @haruspex!

I have done that and got:
View attachment 323496
That is probably the most accurate experimental value for h I'm going to get.

Thank you!
Sorry that is 4 sig fig. To 3 sig fig it is 6.60.

Many thanks!

Depending on the experiment I would say that 7 is a very good result, because it is less that 6% greater than the value in tables :)

ChiralSuperfields
malawi_glenn said:
Depending on the experiment I would say that 7 is a very good result, because it is less that 6% greater than the value in tables :)

How did you collect these data? It is unlikely that you measured the energy and frequency independently. If they are obtained from a photoelectric effect experiment, the honest treatment would be to plot frequency vs. photoelectron energy (or stopping voltage) and extract both the work function and Planck's as the intercept and slope of the regression line. If, as you may have done here, you pre-calculate the work function and then force a zero intercept, you are biasing the data. The linear regression algorithm in Excel should have the freedom to trade slope for intercept.

ChiralSuperfields
kuruman said:
How did you collect these data? It is unlikely that you measured the energy and frequency independently. If they are obtained from a photoelectric effect experiment, the honest treatment would be to plot frequency vs. photoelectron energy (or stopping voltage) and extract both the work function and Planck's as the intercept and slope of the regression line. If, as you may have done here, you pre-calculate the work function and then force a zero intercept, you are biasing the data. The linear regression algorithm in Excel should have the freedom to trade slope for intercept.

I did not collect that data. I think the professor found it online. We were taught to set the intercept equal to zero in Excel since we are not that advanced yet. They may teach us that stuff you are saying in their second- and third-year experimental physics courses.

But thank you mentioning those points, that is helpful to keep in mind.

Many thanks!

kuruman
Callumnc1 said:

I did not collect that data. I think the professor found it online. We were taught to set the intercept equal to zero in Excel since we are not that advanced yet. They may teach us that stuff you are saying in their second- and third-year experimental physics courses.

But thank you mentioning those points, that is helpful to keep in mind.

Many thanks!
That's fine then. Thanks for the clarification.

ChiralSuperfields
kuruman said:
That's fine then. Thanks for the clarification.
Thank you for your help @kuruman!

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