How might we enable the ball to escape? Throw it harder, give it more energy. How hard must we throw it? Just hard enough to get over the top, over the edge of the well. We can find this energy directly by saying that the kinetic energy of the thrown ball must exactly equal the 'potential energy' of the well. From basic physics we know that the potential energy for an object at a height above a surface is:.
Note what extremely important parameter is not in the escape velocity equation: the mass of the moving object. The escape velocity depends only on the mass and size of the object from which something is trying to escape.
The escape velocity from the Earth is the same for a pebble as it would be for the Space Shuttle. Thus, we have created in our imaginary experiment an object from which light cannot escape.
According to the laws of modern physics, in this case according to a postulate of Albert Einstein, nothing, including light, can travel faster than light. Thus, if light cannot escape, then neither can anything else. This is a black hole. Clearly, for any object, we can find a size such that the escape velocity would be greater than the speed of light.
Similarly, for any size object or region of space , we can find a mass such that a mass crammed into that volume of space would be a black hole. The 'size' of the black hole is called the 'Schwarzchild Radius. Question: Imagine that, just like now, the Earth orbits the Sun. Suddenly, I snap my fingers and turn the Sun into a black hole.
What would happen to the Earth? The Kinetic Theory of Gases: What is the speed of a molecule in a gas? Now we know the velocity required to escape from a planet. This is equivalent to knowing the maximum velocity an object can have and still be gravitationally bound to that object.
A gas molecule in a planet's atmosphere is moving quite quickly, with a velocity determined by the temperature of the gas. Thus, in order to know whether a planet is gravitationally strong enough to retain an atmosphere, we next need to know how fast gas molecules move.
Gases are characterized by their temperature, with the temperature determining the average velocity of a gas molecule. According to the kinetic theory of gases developed in the 19th century, the amount of thermal energy per atom or molecule in a gas is given by the formula. Note that in a gas some molecules are moving faster and some slower than average. The distribution of velocities is known as the Boltzmann distribution or the Maxwell speed distribution.
How are the molecules in oxygen gas, the molecules in hydrogen gas, and wate… View Full Video Already have an account? David C. Problem 12 Easy Difficulty Molecules of hydrogen escape from Earth, but molecules of oxygen and nitrogen are held to the surface. Answer Lighter gasses, like hydrogen can escape from Earth's gravity. View Answer. Topics Gases. Chemistry Chapter 12 Gases. Section 1 Characteristics of Gases. Discussion You must be signed in to discuss.
Top Chemistry Educators Stephanie C. University of Central Florida. Allea C. University of Maryland - University College. Karli S. Jake R. University of Toronto. Chemistry Bootcamp Lectures Intro To Chem - Introduction Chemistry is the science o…. Classification and Properties of Matter In chemistry and physics, …. Recommended Videos Have I made any mistakes in my calculations?
The answer to your question comes from Maxwell distribution of speed of the hydrogen molecules. This value is small, but not negligible; in a long enough time, every molecule of hydrogen will escape from Earth's atmosphere. For a last example, you can consider the mass of the molecule of oxygen. Its mass is 16 times bigger than the hydrogen molecule and its root mean square speed is 4 times lower and 24 times lower than the escape speed. This is an intuitive, approximate explanation of why the molecular hydrogen concentration in Earth's atmosphere is really low, while the concentration of other, heavier molecules is higher.
There is a difference in the probability, for a certain molecule, to have a speed greater or equal to the escape speed of the Earth. This influences the rate at which these kind of molecule escape the atmosphere and therefore will lead to a different equilibrium a different concentration for each molecule. The equilibrium concentration of hydrogen in the atmosphere is about 0.
This is a result of mechanisms of production, and destruction chemical reactions, escape. You are right that the RMS velocity of hydrogen is less than the escape velocity - but that doesn't matter.
The thing to keep in mind is that not all molecules have the same velocity. The Maxwell-Boltzmann velocity distribution is of the form. This tells us that there is a small but finite probability of an individual molecule reaching escape velocity. Once that molecule is removed, it won't be coming back, and the velocity distribution will be re-established because the atmosphere will remain at the same temperature.
So there is a slow "leak" of hydrogen from the atmosphere. It is sufficient that that leak be faster than the rate of generation of new hydrogen, for the concentration to drop; eventually, equilibrium is reached. Because Nitrogen and Oxygen have much heavier molecules, they represent a much larger fraction of the atmosphere. The probability that one of their molecules will reach escape velocity is many orders of magnitude smaller than the probability for hydrogen. Thus, over "geological time", almost all hydrogen disappears from the atmosphere.
Note - if you plot the above on a semilog scale you can see just how small the probability of the high velocities is - and then you remember that the upper atmosphere above km or so is actually significantly hotter than the air closer to the surface - under certain conditions, the upper part of the thermosphere can reach temperatures over C during the day.
At that temperature, the probability of hydrogen escaping increases very significantly. This is illustrated in this plot:. Those hot hydrogen molecules and atoms high up in the outermost layers of the atmosphere have a really good chance of escaping Final note - unless the mean free path of the molecule is very large, it will undergo another collision and most likely be sent back to earth.
This is why only the temperature of the very outermost layers of the atmosphere matter for this calculation. The other answers are correct in terms of the principal reason that lighter molecules are much more likely to escape the atmosphere.
However, it seems that the premise of the question and perhaps also of some of the answers and comments is based on an incorrect model of atmospheric escape. Molecules from most parts of the atmosphere would never escape regardless of velocity. The picture below is taken from this document recommended reading and illustrates that escape is basically only possible for molecules above km the exosphere.
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