Calculate the rms speed of free electrons

In summary, the temperature and pressure in a star's atmosphere are given and the task is to calculate the rms speed of free electrons using the formula v=\sqrt{kT/m}. However, this formula is incorrect as it only takes into account one degree of freedom. The correct formula is (3/2)kT. The pressure is given but not needed for the formula. Additional resources for understanding kinetic energy and its calculations are provided.
  • #1
Chele
17
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Hi and thanks for checking this out! :)

Homework Statement


The temperature and pressure in a star's atmosphere are 1.20E6 K and 0.0400 Pa. Calculate the rms speed of free electrons (mass = 9.11 10-31 kg) there.

Homework Equations



What am I doing wrong and why do they give the pressure if that's not needed in the formula!?

The Attempt at a Solution



I'm using this formula:

v=[tex]\sqrt{kT/m}[/tex]

k=1.380658E-23 J/K
T=1.2E6 K
m=9.11E-31 kg

Seems like a simple "plug and chug" type problem. My answer was 4.3E6 m/s. This is not the correct answer.
 
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  • #2
Chele said:
I'm using this formula:

v=[tex]\sqrt{kT/m}[/tex]
That formula is incorrect. The average KE equals (3/2)kT (you must include all three translational degrees of freedom).
 
  • #4

FAQ: Calculate the rms speed of free electrons

What is the formula for calculating the rms speed of free electrons?

The formula for calculating the rms speed of free electrons is v = √(3kT/m), where v is the rms speed, k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of the electron.

Why is it important to calculate the rms speed of free electrons?

Calculating the rms speed of free electrons is important in many fields of science, including physics, chemistry, and engineering. It helps us understand the behavior of electrons in various materials and systems, and is crucial in the design of electronic devices and technologies.

How does temperature affect the rms speed of free electrons?

The rms speed of free electrons is directly proportional to the square root of temperature. This means that as temperature increases, the rms speed also increases. This relationship is described by the formula v = √(3kT/m), where T is the temperature in Kelvin.

Can the rms speed of free electrons be greater than the speed of light?

No, the rms speed of free electrons cannot exceed the speed of light. The speed of light, represented by the letter c, is the maximum speed at which any object or particle can travel in the universe. The rms speed of free electrons is usually much smaller than the speed of light.

How is the rms speed of free electrons related to the average speed of free electrons?

The rms speed of free electrons is related to the average speed by a factor of √3. This means that the rms speed is always greater than the average speed. The average speed of free electrons is calculated by dividing the total speed of all electrons by the number of electrons, while the rms speed takes into account the distribution of speeds among all the electrons.

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