What is the width of a spectral line?

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The discussion centers on the dimensional correctness of a spectral line's width in a homework problem. Participants clarify that the units provided in the problem must be considered when determining the validity of the argument. It is emphasized that the constant in front has specific units, which are essential for the solution. The conversation highlights the importance of adhering to the given units in physics problems. Ultimately, understanding the dimensional analysis is crucial for accurately resolving questions about spectral lines.
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Homework Statement


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Homework Equations

The Attempt at a Solution


The answer is no as it is not dimensionally correct.
Right?
 
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No. You cannot make that argument since you are told explicitly what the units involved are (essentially telling you that the constant in front has units sqrt(K/u)).
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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