# Photoelectrons and Planck's constant

• benca
In summary: You should post your lecture on a dedicated physics forum instead.As you suggested, much too advanced for an introductory physics homework forum.
benca
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.

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

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.

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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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.

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.

That is a much more advanced version, where ## \hbar=c=1 ##, but here we are at the Physics 101 level.
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!

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.

That is a much more advanced version, where ## \hbar=c=1 ##, but here we are at the Physics 101 level.
As you suggested, much too advanced for an introductory physics homework forum.

## 1. What is the photoelectric effect?

The photoelectric effect is a phenomenon in which electrons are emitted from a material when it is exposed to light of a certain frequency or higher. This effect was first observed by Heinrich Hertz in 1887 and was later explained by Albert Einstein in 1905.

## 2. What is the relationship between photoelectrons and Planck's constant?

Planck's constant, denoted by the symbol h, is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. In the photoelectric effect, the energy of a photon is transferred to an electron, causing it to be emitted. The relationship between the maximum kinetic energy of the emitted electron and the frequency of the incident light is given by the equation Kmax = hf - Φ, where Φ is the work function of the material.

## 3. How was Planck's constant determined?

Max Planck determined his constant by studying the relationship between the energy of a blackbody radiation and its frequency. He found that the energy of a blackbody is quantized, meaning it can only take on certain discrete values. By fitting his data with a mathematical formula, Planck was able to calculate the value of his constant as approximately 6.626 x 10^-34 joule seconds.

## 4. Why is Planck's constant important in quantum mechanics?

Planck's constant is a fundamental constant that plays a crucial role in the principles of quantum mechanics. It is used to describe the behavior of particles at the atomic and subatomic level, where classical physics laws no longer apply. It is also used in many equations, such as the Schrödinger equation, which is used to describe the wave function of a quantum system.

## 5. How is Planck's constant relevant in everyday life?

Although Planck's constant is primarily used in quantum mechanics, it has some practical applications in everyday life. For example, it is used in the development of electronic devices such as solar cells and LEDs. It is also used in the study of atomic and molecular spectra, which has applications in fields such as astronomy, chemistry, and medicine.

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