De – Broglie wavelength of O_2

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SUMMARY

The De Broglie wavelength of an O2 molecule is calculated using the formula λ = h/p, where h is Planck's constant and p is the momentum. For non-relativistic conditions, the momentum is derived from the kinetic energy equation, p2/2m = 3kBT/2. The resulting wavelength is determined to be 2.6 x 10-11 m, confirming option (a) as correct.

PREREQUISITES
  • Understanding of De Broglie wavelength concept
  • Familiarity with Planck's constant (h)
  • Knowledge of kinetic energy equations
  • Basic principles of non-relativistic physics
NEXT STEPS
  • Research the implications of De Broglie wavelength in quantum mechanics
  • Learn about the applications of Planck's constant in various physical phenomena
  • Explore the relationship between temperature and molecular speed in gases
  • Investigate the differences between relativistic and non-relativistic momentum
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Students studying quantum mechanics, physicists interested in molecular behavior, and educators teaching the principles of wave-particle duality.

Pushoam
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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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