Concept explainers
(a)
The temperature at which the root mean square speeds for
(a)
Explanation of Solution
Given:
The escape speed of the surface of the planet is
Formula used:
Write the expression for the rms speed of the molecule.
Here,
Equate
Here,
Solve the above equation for
Calculation:
Substitute
Conclusion:
The temperature is
(b)
The temperature at which the root mean square speeds for
(b)
Explanation of Solution
Given:
The escape speed of the surface of the planet is
Formula used:
Write the expression for the rms speed of the molecule.
Here,
Calculation:
Substitute
Conclusion:
The temperature is
(c)
The reason for the low hydrogen in the earth atmosphere.
(c)
Explanation of Solution
Given:
The escape speed of the surface of the planet is
Introduction:
All the giant planets like Jupiter, Saturn, Uranus and Neptune contains helium and hydrogen in the atmosphere of the giant planets.
Earth contains low amount of hydrogen in the atmosphere because hydrogen gas is very light as compared to other elements and has high escape speed at the high temperature and thus hydrogen gas escapes from the earth’s atmosphere.
Conclusion:
The hydrogen gas molecules attain greater escape speed than other elements and therefore earth’s atmosphere contains low amount of hydrogen.
(d)
(d)
Explanation of Solution
Given:
The escape speed of the surface of the planet is
Gravity on moon is one-sixth the gravity on moon.
Radius of earth is
Formula used:
Substitute
Substitute
Here,
Calculation:
Substitute
Thus, the temperature of
Substitute
Conclusion:
The escape speed is low on moon as the acceleration due to gravity is less there. Thus the largerpercentage of molecules moves with escape speed.
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Chapter 17 Solutions
Physics for Scientists and Engineers, Vol. 3
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