One-Dimensional distribution of Molecular Velocity Questioin

In summary, the formula for calculating the function for N2 at 300K is d(vx)= (m/2pikT)^1/2 exp(-(mv^2/2kT)), where the Boltzmann constant is 1.3806503 × 10-23 m2 kg s-2 K-1 and the mass of N2 is 0.0280 kg. However, the mass used for N2 is incorrect as it should be the mass of one molecule, not of one mole. This may result in an incorrect value of 0 when calculating the exponential part of the equation.
  • #1
ramsharmjarm
7
0
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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  • #2
The mass you use for N2 is incorrect. It should be the mass of one molecule, not of one mole.
 

1. What is a one-dimensional distribution of molecular velocity?

A one-dimensional distribution of molecular velocity refers to the probability distribution of the velocities of molecules in a single direction. It is used to describe the motion of particles in a gas or liquid, and is an important concept in the study of thermodynamics and statistical mechanics.

2. How is the one-dimensional distribution of molecular velocity calculated?

The one-dimensional distribution of molecular velocity is calculated using the Maxwell-Boltzmann distribution, which takes into account the mass and temperature of the molecules. This distribution describes the percentage of molecules with a given velocity at a specific temperature.

3. What is the significance of the one-dimensional distribution of molecular velocity?

The one-dimensional distribution of molecular velocity is significant because it provides information about the kinetic energy and speed of molecules in a gas or liquid. It also helps to understand the behavior of gases and liquids, and is used in various applications such as gas dynamics and chemical reactions.

4. How does the one-dimensional distribution of molecular velocity differ from the three-dimensional distribution?

The one-dimensional distribution of molecular velocity describes the velocities of molecules in a single direction, while the three-dimensional distribution considers the velocities in all three dimensions. The one-dimensional distribution is a simplified version of the three-dimensional distribution and is often used in basic calculations and models.

5. Can the one-dimensional distribution of molecular velocity be applied to all types of molecules?

Yes, the one-dimensional distribution of molecular velocity can be applied to all types of molecules, including atoms, molecules, and ions. It is a fundamental concept in the study of gases and liquids and is used to describe the behavior of particles in these systems regardless of their composition.

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