Griffiths Quantum Mechanics Problem 1.18: Characteristic Size of System

In summary, the conversation discusses the concept of intermolecular distance and its relation to the volume and number of particles in a system. While one person envisions the particles as a sphere, the other imagines them as a box. This difference results in a significant factor of (4π/3)^2/5 ≈ 1.8. The conversation also touches on the idea of filling a box with oranges and the importance of choosing an appropriate shape for computational ease.
  • #1
yucheng
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Homework Statement
The characteristic size (length) of ideal gas where quantum effects are non-negligible is the intermolecular distance, ##d##
Relevant Equations
##pV = Nk_BT##
intermolecular distance means distance between particles. So, I imagine a sphere.

$$\frac{4}{3} \pi d^3 = \frac{V}{N}$$

However, Griffitfhs pictures a box instead, where

$$d^3 = \frac{V}{N}$$

And the difference between both models is a factor of ##(4\pi/3)^{2/5} \approx 1.8##, which is fairly large...
 
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  • #2
If you fill a box with oranges, does it fill the space completely? Griffiths is correct
 
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  • #3
hutchphd said:
If you fill a box with oranges, does it fill the space completely? Griffiths is correct
I think I understand... So I guess I should have searched for a reliable shape to fill the whole space!
 
  • #4
And usually we imagine the box to be square, for computational convenience...
 
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FAQ: Griffiths Quantum Mechanics Problem 1.18: Characteristic Size of System

1. What is the purpose of Griffiths Quantum Mechanics Problem 1.18?

The purpose of this problem is to understand the concept of characteristic size of a system in quantum mechanics. It involves calculating the average position and momentum of a particle in a box and using these values to determine the characteristic size of the system.

2. How is the characteristic size of a system determined in this problem?

In this problem, the characteristic size of a system is determined by finding the root-mean-square (RMS) position of the particle in a box. This is calculated by taking the square root of the average of the squared position values.

3. What is the significance of the characteristic size of a system in quantum mechanics?

The characteristic size of a system is an important concept in quantum mechanics as it represents the scale at which the quantum behavior of a particle is observed. It also helps in understanding the confinement of particles in a potential well and the quantization of energy levels.

4. Can the characteristic size of a system be measured experimentally?

Yes, the characteristic size of a system can be measured experimentally by measuring the RMS position of a particle in a box. This can be done using various techniques such as scattering experiments or spectroscopy.

5. Are there any real-world applications of understanding the characteristic size of a system in quantum mechanics?

Yes, the concept of characteristic size of a system has many real-world applications, such as in the design of electronic devices and materials, understanding the behavior of atoms and molecules in a confined space, and in the development of quantum technologies.

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