How to find von-Klitzing constant based on graph?

Thread starter john chen
Start date Apr 21, 2019
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Constant Graph Physics Quantum hall effect Quantum particles Quantum physics

In summary, the von-Klitzing constant, also known as the quantum Hall resistance, is a fundamental physical constant used to define the SI unit for electrical resistance. It relates the resistance of a two-dimensional electron gas to the Planck constant and the electron charge, and has a value of approximately 25,812.807 ohms. It can be calculated by plotting the resistance of a two-dimensional electron gas against the applied magnetic field and measuring the slope of the resulting graph. The constant has important applications in metrology and is not affected by the material used for measurement. However, factors such as temperature, sample imperfections, and measurement errors can affect its value and must be carefully controlled for accurate measurement.

Apr 21, 2019

john chen

Homework Statement: How do i estimate the von-klitzing constant based on figure 2

Relevant Equations: Rk = h/e^2 (von-klizing constant)

Hi all,

Given that the question:

From what i know

, I am not sure how this equation can help me estimate the von-klitzing constant? Or is there another way? Thanks!

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Apr 21, 2019

Nate810

The answer to this question is that the von-Klitzing constant cannot be estimated using an equation. It is a fundamental constant of nature and must be measured experimentally. The exact value of the constant is 8.854187817 × 10^−12 A⋅s/Vm.

Related to How to find von-Klitzing constant based on graph?

1. How is the von-Klitzing constant related to graphing?

The von-Klitzing constant, denoted as R_K, is a fundamental physical constant that relates to the quantization of the Hall resistance in a two-dimensional electron gas. This quantization can be observed and measured through graphing the Hall resistance as a function of the magnetic field.

2. What is the formula for calculating the von-Klitzing constant?

The formula for calculating the von-Klitzing constant is R_K = h/e², where h is the Planck constant and e is the elementary charge. This formula is based on the quantum Hall effect, which states that the Hall resistance is quantized in units of h/e².

3. What is the significance of the von-Klitzing constant?

The von-Klitzing constant is significant because it provides a precise and universal standard for electrical resistance. It is used in metrology and is considered to be one of the most accurately known physical constants. It also has important implications in the study of condensed matter physics and has been used to further our understanding of quantum mechanics.

4. How can I find the von-Klitzing constant from a graph?

To find the von-Klitzing constant from a graph, you will need to plot the Hall resistance (R_H) on the y-axis and the magnetic field (B) on the x-axis. Then, find the slope of the linear portion of the graph, which should be equal to R_K. This can be done by dividing the change in R_H by the change in B. Alternatively, you can use the formula R_K = h/(e x slope) to calculate the constant.

5. Are there any experimental considerations when finding the von-Klitzing constant from a graph?

Yes, there are a few experimental considerations to keep in mind when finding the von-Klitzing constant from a graph. These include ensuring that the sample is in the quantum Hall regime, taking multiple measurements at different magnetic fields to confirm the linearity of the graph, and minimizing any sources of error such as temperature fluctuations or contact resistance. It is also important to use precise and accurate measurement equipment for reliable results.