Today's Q

[ceagle]

Alrighty, cats n kittens! Here's a ponderance ya might find fun to deduce... :>

We know that there's the periodic table of elements, and on that table the first two lightest ones Hydrogen and Helium are too light to stay upon the earth if released from a container or compound. On a recent science show, they stated that we would lose virtually all of the Earth's hydrogen at this rate in about 1.2 billion years.

On Mars, the gravity is only 38% of Earth's, so... which elements would fall into the category of being too light to remain on Mars? :D

Comments

[austin-dern.livejournal.com]

That's a pretty basic astrophysics/planetary science problem, at least if you don't want to get into too fine a detail.

The routine to work it out is: planetary atmospheres are at some (average) temperature. Given that temperature, then you know the average kinetic energy of the gas particles, since that's just a scalar multiple of the temperature. Once you know the average kinetic energy of the gas particles, you know the average speed of the gas particles, since the kinetic energy is half the mass times the square of the speed of the particles at these temperatures.

Now, it's easy to work out the escape velocity of a particle from the surface of the planet. If that's lower than the average molecular speed, forget it; the atmosphere's gone. But even if it's higher than the average molecular speed ... well, when molecules get bumped above that speed, they're going to leave (sooner or later). The escape velocity has to be considerably higher than the mean molecular speed to have a chance of sticking around for an indefinitely long lifetime. A rule of thumb (used in Introductory Astronomy and Astrophysics, Zelik and Smith, a pretty good introduction to the subjects) is you'll see molecules stick around if the escape velocity is more than ten times the mean molecular speed.

For Mars's temperatures, this implies that oxygen, nitrogen, carbon dioxide, and xenon have indefinite lifetimes. Hydrogen, helium, water, ammonia, and methane are gone. (Important to remember here: oxygen and nitrogen appear as diatomic molecules, making their molecular weights higher than, say, water or nitrogen.) Something halfway between the weight of water and (diatomic) oxygen is right about at the border for Mars to keep.

The equation for the relationship is that a molecule of mass m will stick around indefinitely around a planet with mass M and radius R if the atmospheric temperature G satisfies:

T ≤ (G M m) / (100 k R)

Where G is the gravitational constant and k is the Boltzman constant. The 100 reflects that ten-times-the-velocity margin.

[sebkha.livejournal.com]

Well, you just answered the hell out of that question. Next!

What can I say, but...

[c-eagle.livejournal.com]

W o w ... ^v^


...so um, I guess lithium is not long for Mars, ah? :D


Ununquadium, sir! Ununquadium!