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Interstellar space has an average temperature of about 10 K , and an average density of hydrogen atoms of about one hydrogen atom per cubic meter. Calculate the mean free path of hydrogen atoms in interstellar space. Use ????=100 pm as the diameter of a hydrogen atom.

Respuesta :

Answer:

[tex]2.2508\times 10^{19} m[/tex] meter the mean free path of hydrogen atoms in interstellar space.Explanation:

The mean free path equation is given as:

[tex]\lambda =\frac{1}{\sqrt{2}\pi d^2 n}[/tex]

Where"

d = diameter of hydrogen atom in meters

n =  number of molecules per unit volume

We are given: d = 100 pm = [tex]100\times 10^{-12}= 10^{-10} m[/tex]

[tex]n = 1 m^{-3}[/tex]

[tex]\lambda =\frac{1}{\sqrt{2}\pi (10^{-10} m)^2\times 1 m^{-3}}[/tex]

[tex]\lambda =2.2508\times 10^{19} m[/tex]

[tex]2.2508\times 10^{19} m[/tex] meter the mean free path of hydrogen atoms in interstellar space.

Lanuel

The mean free path of hydrogen atoms in interstellar space is [tex]2.25 \times 10^{17}[/tex] meters.

Given the following data:

  • Temperature = 10 Kelvin.
  • Number of moles = 1 [tex]m^{-3[/tex]
  • Diameter of a hydrogen atom = 100 picometer.

Conversion:

Diameter of a hydrogen atom = 100 pm =  [tex]100 \times 10^{-12} = 10^{-10}[/tex] meters.

To calculate the mean free path of hydrogen atoms in interstellar space:

Mathematically, the mean free path of an atom is given by the formula:

[tex]\lambda = \frac{1}{\sqrt{2}\pi d^2 n }[/tex]

Where:

  • [tex]\lambda[/tex] is the mean free path of an atom.
  • d is the diameter of an atom.
  • n is the number of moles.

Substituting the given parameters into the formula, we have;

[tex]\lambda = \frac{1}{\sqrt{2}\; \times \;3.142 \;\times\; (10^{-10})^2 \;\times\;1 }\\\\\lambda = \frac{1}{1.4142\; \times\;3.142 \;\times\; 1^{-18}}\\\\\lambda = \frac{1}{4.44 \;\times\; 10^{-18}}\\\\\lambda = 2.25 \times 10^{17}\; meters[/tex]

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