Mean Free Path of an Electron in Mercury Vapour

In summary, the Mean Free Path of an Electron in Mercury Vapour is the average distance an electron can travel before colliding with another particle. This is affected by temperature, pressure, and density, and can be calculated using a specific formula. It is a significant factor in understanding the behavior of electrons in mercury vapour and differs from other gases due to the size and density of mercury atoms.
  • #1
jameson2
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Homework Statement


Estimate the mean free path of an electron in mercury vapour at a temperature of 160 degrees C, where the vapour pressure is 11.28 mmHg
It gives the standard atmospheric pressure as 761.84 mmHg.

Homework Equations


Mean free path= (Boltzmann's constant times temperature)/(sqrt(2)*pi*(d^2)*p)
where d is the diameter of the molecule and p is the pressure.


The Attempt at a Solution


I have: Boltzmann's constant= 1.38x10^-23
T=273+160=433K
d=302x10^-12 metres
p=(11.28/761.84)*101325 Pa
(I think these are all the right units to use)

So I fill these into the formula and get 9.834x10^-6 m as my value for mean free path. I have nothing to compare this to, so I have no idea whether this is right or way off the mark.
 
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  • #2


Thank you for your post regarding the estimation of the mean free path of an electron in mercury vapour at a temperature of 160 degrees C. Your calculations seem to be correct and your estimated value of 9.834x10^-6 m is reasonable.

To provide some context, the mean free path is a measure of the average distance an electron travels before colliding with another particle. In a gas, the mean free path is inversely proportional to the pressure and directly proportional to the temperature. This means that as the pressure decreases or the temperature increases, the mean free path will increase.

In the case of mercury vapour at 160 degrees C, the pressure is relatively low at 11.28 mmHg, which results in a longer mean free path compared to higher pressure systems. Additionally, the temperature is quite high, further increasing the mean free path.

It is important to note that the mean free path is an average value and the actual distance an electron travels before colliding can vary significantly. Furthermore, the mean free path in a gas can also depend on other factors such as the composition of the gas and the energy of the electrons.

Overall, your estimation of the mean free path in mercury vapour at 160 degrees C is reasonable and provides a good understanding of the average distance an electron can travel before colliding with another particle in these conditions. I hope this helps clarify your calculations and provides some context for your estimation. Keep up the good work in your scientific studies!
 

What is the Mean Free Path of an Electron in Mercury Vapour?

The Mean Free Path of an Electron in Mercury Vapour is the average distance that an electron can travel before colliding with another particle. It is a measure of how far an electron can move freely without being disturbed.

What factors affect the Mean Free Path of an Electron in Mercury Vapour?

The Mean Free Path of an Electron in Mercury Vapour is affected by temperature, pressure, and the density of mercury vapour. Higher temperatures and lower pressures result in longer mean free paths, while higher densities decrease the mean free path.

How is the Mean Free Path of an Electron in Mercury Vapour calculated?

The Mean Free Path of an Electron in Mercury Vapour can be calculated using the following formula: λ = 1/(√2πd^2n), where λ is the mean free path, d is the diameter of the mercury atom, and n is the number of mercury atoms per unit volume.

What is the significance of the Mean Free Path of an Electron in Mercury Vapour?

The Mean Free Path of an Electron in Mercury Vapour is an important parameter in understanding the behavior of electrons in the presence of mercury vapour. It helps in predicting the electrical conductivity and other properties of mercury vapour under different conditions.

How does the Mean Free Path of an Electron in Mercury Vapour differ from other gases?

The Mean Free Path of an Electron in Mercury Vapour is shorter compared to other gases due to the large size and high density of mercury atoms. This results in more frequent collisions between electrons and mercury atoms, decreasing the mean free path.

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