Determination of planck's constant

In summary, the conversation is discussing a graph of voltage versus frequency and how to use it to estimate the value of Planck's constant. The equation eV_s=\frac{1}{2}mv^2 is mentioned and rearranged to solve for h. The values of m and c are also provided, but a mistake is pointed out in the calculation of the gradient. The conversation ends with a reminder to be careful with units when calculating the gradient.
  • #1
Ry122
565
2
I have a graph of voltage verse frequency.
Given that the charge of an electron = 1.6 x 10^-19 I need to obtain an estimate of the value Planck's constant. What equation do I need to use? Do I find the gradient of the graph?
 
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  • #2
What is the experiment that led to these measurements (this graph)?
[I have a guess... but you should really describe it.]
 
  • #3
its the stopping voltage versus frequency for a metal surface.
The only part of the graph shown is from 5.4 to 6.8 f(X 10^14) and .26 to .85 volts. The graph is linear.
 
  • #4
the work done in stopping the electron is equal to the kinetic energy lost...
that is,
[itex]eV_s=\frac{1}{2}mv^2[/tex]

so from [itex]hf=hf_0+\frac{1}{2}mv^2[/itex]=>[itex]hf=hf_0+eV_s[/itex]

rearrange and make it into the form you want...
 
  • #5
How can I solve for h when h is on both sides of the equation?
 
  • #6
[itex]eV_s=hf-hf_0[/itex]
[itex]V_s=\frac{h}{e}f-\frac{h}{e}f_0[/itex]

Y=MX+C, can you see what M and C are?
 
  • #7
I can't see what they are.
The values are
m = .421428
c = -2.2757 x 10^14
 
  • #8
Well from [itex]V_s=\frac{h}{e}f-\frac{h}{e}f_0[/itex]

if a graph of [itex]V_s[/itex] and f is drawn, then the gradient,m. would be equal to the fraction: [itex]\frac{h}{e}[/itex] and so you know what e is, find h
 
  • #9
I tryed this but but solving for h in m=h/e does not give Planck's constant.
 
  • #10
Are you being careful with your units when you are calculating your gradient?

Remember that your frequency scale will probably be (x 10^14) Hz

You should get a much smaller gradient.
 

1. What is 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.

2. Why is it important to determine Planck's constant?

Determining Planck's constant is crucial in understanding the behavior of particles at the atomic and subatomic level. It is also used in many technological applications, such as the development of semiconductors and lasers.

3. How is Planck's constant determined?

One method of determining Planck's constant is through the photoelectric effect, which involves measuring the energy of photons emitted from a metal surface when light of different frequencies is shone on it. By plotting the data and using the equation E = hf, where E is the energy of the photon, h can be calculated.

4. What is the current accepted value of Planck's constant?

The current accepted value of Planck's constant is 6.62607015 x 10^-34 joule seconds (J·s), as determined by the International Committee for Weights and Measures in 2019.

5. Has Planck's constant always had the same value?

No, the value of Planck's constant has been refined over time through various experiments and technological advancements. The current accepted value is considered to be extremely accurate, but it is still subject to future revisions as technology advances.

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