De – Broglie wavelength of O_2

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The De Broglie wavelength of an O2 molecule is calculated using the formula λ = h/p, assuming non-relativistic speeds. The momentum p is derived from the kinetic energy equation, leading to the conclusion that λ = 2.6 x 10^-11 m. The calculation appears to be accurate, confirming option (a) as correct. This demonstrates the application of quantum mechanics to molecular physics. The discussion highlights the importance of understanding molecular behavior at small scales.
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Homework Statement


upload_2017-12-26_17-54-23.png


Homework Equations

The Attempt at a Solution

[/B] De – Broglie wavelength of ## O_2 ## molecule is ## \lambda = \frac h p ##

Assuming that the speed of molecule is small enough to take non – relativistic calculation,

## \frac { p^2}{2m} = \frac { 3 k_B T }2 ##

## \lambda = 2.6 * 10^{-11}~ m ##

So, the correct option is (a).
 

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Looks right.
 
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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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