Amplitude and inter atomic separation

In summary, to calculate the root mean amplitude for a system with given parameters, we can use the formula √(kBT/D) and follow the steps of converting the unit of inter atomic separation, calculating the value, and converting it to a percentage. This will give us the root mean amplitude as 0.9% of the inter atomic separation.
  • #1
ibysaiyan
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Homework Statement


The question goes something like this:
What % of inter atomic separation is the root mean amplitude.
The data given is:
Inter atomic separation : 0.29nm , T =300k , D = 20 N/m , Aluminium atomic weight 27 g/mole.
How do I proceed I have no idea on how to relate mean inter atomic separation and rms of the amplitude.


Homework Equations



Formula to calculate Root mean amplitude is : √KbT/D

The Attempt at a Solution



As above.
 
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  • #2


Thank you for your question. It seems like you are trying to calculate the root mean amplitude for a system with given parameters. Here are the steps you can follow to proceed with the calculation:

1. First, let's define the parameters given in the problem:
- Inter atomic separation: 0.29nm
- Temperature (T): 300K
- Spring constant (D): 20 N/m
- Aluminium atomic weight: 27 g/mole

2. Next, let's convert the inter atomic separation from nanometers to meters, since the spring constant is given in N/m:
0.29nm = 0.29 x 10^-9m

3. Now, we can use the formula for root mean amplitude to calculate the value:
√(kBT/D) = √((1.38x10^-23 J/K)(300K)/(20 N/m)) = 2.6 x 10^-12 m

4. Finally, to get the percentage of inter atomic separation, we can divide the root mean amplitude by the inter atomic separation and multiply by 100:
(2.6 x 10^-12 m / 0.29 x 10^-9 m) x 100 = 0.9%

Therefore, the root mean amplitude is 0.9% of the inter atomic separation. I hope this helps you with your problem. Let me know if you have any further questions. Good luck with your calculations!
 

1. What is amplitude in relation to inter atomic separation?

Amplitude refers to the maximum displacement from the equilibrium position of a wave. In the context of inter atomic separation, amplitude is a measure of the distance between two adjacent atoms in a solid material when they are vibrating at their maximum displacement.

2. How does amplitude affect inter atomic separation?

The amplitude of a wave is directly proportional to the inter atomic separation. This means that as the amplitude increases, the distance between adjacent atoms also increases. Similarly, a decrease in amplitude results in a decrease in inter atomic separation.

3. What is the relationship between inter atomic separation and atomic bonding?

The inter atomic separation between two atoms is determined by the type and strength of atomic bonding between them. In general, stronger bonds result in smaller inter atomic separations, while weaker bonds result in larger separations.

4. How is inter atomic separation measured?

Inter atomic separation is typically measured in units of distance, such as nanometers or angstroms. This can be done using techniques such as X-ray diffraction, scanning tunneling microscopy, or atomic force microscopy.

5. What factors can affect inter atomic separation?

The inter atomic separation between two atoms can be influenced by a variety of factors, including temperature, pressure, and the type of material. For example, increasing temperature can cause atoms to vibrate more, resulting in a larger inter atomic separation. Additionally, changes in the atomic structure or composition of a material can also impact inter atomic separation.

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