One-Dimensional distribution of Molecular Velocity Questioin

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SUMMARY

The discussion focuses on calculating the one-dimensional distribution of molecular velocity for nitrogen (N2) at 300K using the Boltzmann distribution formula. The correct mass to use in the equation is the mass of a single nitrogen molecule, approximately 4.68 × 10-26 kg, rather than the molar mass of 0.0280 kg. Participants encountered issues with the exponential term in the equation yielding zero due to incorrect mass input, emphasizing the importance of using molecular mass in calculations.

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  • Understanding of the Boltzmann distribution
  • Knowledge of molecular mass calculations
  • Familiarity with the concept of temperature in kinetic theory
  • Basic proficiency in exponential functions and their behavior
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  • Research the correct molecular mass of nitrogen for kinetic calculations
  • Learn about the implications of temperature on molecular velocity distributions
  • Explore the use of the Boltzmann constant in thermodynamic equations
  • Investigate numerical methods for evaluating exponential functions in computational physics
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ramsharmjarm
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1. Homework Statement [/b]

Calculate the function for N2 at 300k

d(vx)= (m/2pikT)^1/2 exp(-(mv^2/2kT)

I have to be able to use this equation for varying velocity from -1500 m/s to 1500 m/s

The Attempt at a Solution



Boltzmann constant = 1.3806503 × 10-23 m2 kg s-2 K-1
N2 mass= 0.0280 kg

So I am plugging these 2 values in the equation, but i keep getting 0 when i do the exp(mv^2/2kt part). e to the power of such a high number gives me 0 and that high number comes from my denominator being such as small value, so I am no sure what to do.

I have uploaded question formula picture incase its not clear.
 

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The mass you use for N2 is incorrect. It should be the mass of one molecule, not of one mole.
 

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