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Q. 25

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 567

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Short Answer

The atmosphere of the sun consists mostly of hydrogen atoms (not molecules) at a temperature of . What are (a) the average translational kinetic energy per atom and (b) the rms speed of the atoms?

(a) The average translational kinetic energy per atom is

(b) The rmsspeed of atom is

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Step by Step Solution

Step :1 Introduction (part a)

(a) The average translational kinetic energy of a molecule with mass m and velocity v is The average translational kinetic energy of a molecule is affected by its temperature, hence it is related to the temperature t per molecule in the manner

Where is Boltzmann's constant and in unit its value is

Plug the values for and into equation (1) to get the energy for the atom

Step :2  Energy (part b)

(b)The transitional energy depends on the temperature only not the mass of the gas. The molecule with mass and velocity has an average translational kinetic energy and it is given by equation in the form

As shown, both equations have the same left side, so we can use these expressions to get an equation for root mean square velocity

Step :3 Mass of hydrogen atom

The mass of the hydrogen atom is the same for one proton . Now, we plug the values for and into equation (3) to get

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