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In summary, the question is asking how many ways there are to group 6 distinguishable molecules into 3 different energy levels, with specific numbers of molecules in each level. The solution involves dividing the number of ways obtained for 3 different energy levels by the factorial of the number of molecules in each level. A more general question is also posed, asking how many ways N numbered balls can be grouped into three sets with specific numbers of balls in each set. The solution involves choosing the first set, then choosing the second set in a certain way.
  • #1
patcho
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Hi,

I'm not quite sure about this question:

'How many Ways can 6 distinguishable molecules be placed in 3 different energy levels with 3 molecules in the 1st level, 2 in the 2nd level and 1 in the 3rd level, ignoring energy required?'

If it was just how many ways to place them in 3 different levels it would be easy but how to always keep 3 molecules in the first, 2 in the 2nd and 1 in the first confuses me.

I know that the number of Ways is less than before and I'm thinking along the lines of having to divide the number obtained if it was just 3 different energy levels, by 3!2!1! (the number of molecules in each level). This gives: W=10 which I think is very wrong!

Any help appreciated!

:smile:
 
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  • #2
Take a slightly more general question:

How many ways can N numbered balls be grouped into three sets such that the first group contains [itex]n_1[/itex] balls, the second set [itex]n_2[/itex] balls and the third set [itex]N-n_1-n_2[/itex] balls?

Hint: How many ways are there to choose the first set? After that, in how many ways can you choose the second set?
 
  • #3


Hi there,

Thank you for your question. It seems like you are trying to figure out the number of possible arrangements for 6 distinguishable molecules in 3 different energy levels, with specific numbers of molecules in each level.

In this case, you can use the concept of combinations to find the number of ways to place the molecules. The formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of objects and r is the number of objects being chosen.

In this problem, we have 6 molecules and we want to choose 3 for the first level, 2 for the second level, and 1 for the third level. So, the number of ways to place these molecules would be:

6C3 * 3C2 * 1C1 = (6! / (3! * (6-3)!) * (3! / (2! * (3-2)!) * (1! / (1! * (1-1)!)
= (6*5*4 / (3*2*1)) * (3*2 / (2*1)) * (1 / (1*0))
= 20 * 3 * 1
= 60

So, there are 60 ways to place 6 distinguishable molecules in 3 different energy levels with 3 molecules in the first level, 2 in the second level, and 1 in the third level.

I hope this helps clarify the concept for you. If you have any further questions, please feel free to ask. Best of luck with your studies!
 

1. How do molecules naturally arrange themselves into specific patterns?

Molecules are constantly moving and interacting with one another due to various forces, such as electromagnetic forces. This movement creates a balance between these forces, resulting in specific patterns or arrangements of molecules.

2. Can we control the placement of molecules in a specific way?

Yes, scientists have developed techniques such as molecular self-assembly and nanolithography to control the placement of molecules in a specific way. These methods utilize external forces to arrange molecules into desired patterns.

3. What is the significance of studying ways to place molecules?

Understanding and controlling the placement of molecules is crucial in various fields such as nanotechnology, materials science, and medicine. It allows us to create new materials with unique properties, design more efficient drug delivery systems, and advance technologies such as computer chips and solar cells.

4. Are there limitations to the ways we can place molecules?

Yes, there are limitations to the ways we can place molecules. These limitations include the size and shape of the molecules, the type of surface they are being placed on, and the strength of the binding forces between the molecules and the surface.

5. What advancements have been made in the field of placing molecules?

In recent years, scientists have made significant advancements in placing molecules in specific ways. These include developing new techniques and tools for placing molecules, as well as discovering new ways to manipulate and control their placement, such as using light or electrical fields.

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