A particle on the surface of the Earth can "escape" the Earth's gravitation and continue to move away from the Earth forever, if it has a sufficient speed (called the escape speed). (a) Determine the escape speed (in m/s) if the particle is an oxygen molecule. Use 6.37 × 106 m for radius of the Earth. m/s (b) Determine the temperature (in K) at which the rms speed of the oxygen molecule is 13 times the escape speed. T = K (c) What If? The Universe is composed of 75% hydrogen and 25% helium by mass, yet these gases are not found in the Earth's atmosphere. Calculate the temperatures (in K) for which the minimum escape kinetic energy is nine times the average kinetic energy of hydrogen (H₂) molecules and helium atoms. TH₂ THE = = K K

A particle on the surface of the Earth can "escape" the Earth's gravitation and continue to move away from the Earth forever, if it has a sufficient speed (called the escape speed). (a) Determine the escape speed (in m/s) if the particle is an oxygen molecule. Use 6.37 × 106 m for radius of the Earth. m/s (b) Determine the temperature (in K) at which the rms speed of the oxygen molecule is 13 times the escape speed. T = K (c) What If? The Universe is composed of 75% hydrogen and 25% helium by mass, yet these gases are not found in the Earth's atmosphere. Calculate the temperatures (in K) for which the minimum escape kinetic energy is nine times the average kinetic energy of hydrogen (H₂) molecules and helium atoms. TH₂ THE = = K K

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Diatomic Gas

Molecule, is a collection of two or more atoms together (which constitute the smallest observable unit) into a pure material. There are some ways to represent the structure of a molecule. Factor symbols represent atoms in Lewis structures, and dots represent electrons that accompany them. A pair of mutual electrons (covalent bond) may be represented by a single dash. The ball-and-stick model depicts the spatial structure of the atoms better.

Question

A particle on the surface of the Earth can "escape" the Earth's gravitation and continue to move away from the Earth forever, if it has a sufficient speed (called
the escape speed).
(a) Determine the escape speed (in m/s) if the particle is an oxygen molecule. Use 6.37 x 106 m for radius of the Earth.
m/s
(b) Determine the temperature (in K) at which the rms speed of the oxygen molecule is 13 times the escape speed.
T =
K
(c) What If? The Universe is composed of 75% hydrogen and 25% helium by mass, yet these gases are not found in the Earth's atmosphere. Calculate the
temperatures (in K) for which the minimum escape kinetic energy is nine times the average kinetic energy of hydrogen (H₂) molecules and helium atoms.
K
K
TH2
THE

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Step 1: Part (a) - Finding the value of the escape speed of an oxygen molecule:

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Step 2: Part (b) - Finding temperature at which the rms speed of oxygen molecule is 13 times escape speed:

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Step 3: Part (b) - Finding temperature at which the rms speed of oxygen molecule is 13 times escape speed:

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Step 4: Part (c) - Compute the relation for the average energy of a particle:

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Step 5: Part (c) - Finding the value of temperature for hydrogen molecule:

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Step 6: Part (c) - Finding the value of temperature for helium molecule:

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