Help with Maxwell-Boltzmann Energy Distribution stuff

In summary, the problem at hand involves determining the fractions of electrons with energy between E=2ev and E=3ev by using an integral, after simplifying and factoring all constants. The solution requires dividing the interval into five equal segments and approximating the area under each rectangle, similar to Riemann sums. The gamma function may also be useful in solving this integral.
  • #1
eissa
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Homework Statement


I am trying to determine the fractions of electrons with energy between E=2ev and E=3ev. to simplify the equation I have substituted everything out leaving an integral which is what I need help with.


Homework Equations


f(x)=(Sqrt(x)*e^-x)dx
-integrate from x=1 to x=1.5
-divide into 5 parts

The Attempt at a Solution


After simplifying and factoring all constants the above equation is what I'm left with. I'm quite confused with this integral but was told by my professor to divide the interval into five equal segments and approximate the area under each rectangle. I remember doing something similar to this in a previous calc class involving riemann sums, whereby I believe the rectangles were also used, but I cannot seem to recall the necessary steps to solving this definite integral. Any ideas and suggestions would be great.
 
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  • #2
This integral looks like the gamma function except that the limits of integration are different. I'm not sure if that helps you or not, but I believe you could find some help by learning more about the gamma function.

But I'd probably just use an integral table because I can never remember how to do Riemann sums when I need to. lol
 

1. What is the Maxwell-Boltzmann energy distribution?

The Maxwell-Boltzmann energy distribution is a statistical distribution that describes the average distribution of energies among particles in a gas at a given temperature. It is used to model the behavior of gases and their individual particles.

2. How is the Maxwell-Boltzmann energy distribution calculated?

The Maxwell-Boltzmann energy distribution is calculated using the following formula: f(E) = (2/pi)^(1/2) * (E/kT)^(3/2) * e^-E/kT, where f(E) is the frequency of particles with a given energy E, k is the Boltzmann constant, and T is the temperature in Kelvin.

3. What does the Maxwell-Boltzmann energy distribution tell us about a gas?

The Maxwell-Boltzmann energy distribution tells us about the average distribution of energies among particles in a gas. It can provide information about the most probable energy of particles, the average energy, and the range of energies present in the gas.

4. How does temperature affect the Maxwell-Boltzmann energy distribution?

Temperature has a significant impact on the Maxwell-Boltzmann energy distribution. As temperature increases, the distribution shifts to the right, meaning that there is a higher proportion of particles with higher energies. This is because higher temperatures increase the kinetic energy of particles, leading to a wider range of energies in the gas.

5. What are some real-world applications of the Maxwell-Boltzmann energy distribution?

The Maxwell-Boltzmann energy distribution is used in many fields, including thermodynamics, statistical mechanics, and chemical kinetics. It is also used in the study of gas dynamics, such as in the design of rocket engines and in the development of new materials for energy storage. Additionally, it is used in the development of new technologies, such as gas sensors and semiconductor devices.

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