Dissociation of H2O due to Photon energy.

[JJamison]

I can't figure out how to do this question: Given that the rate of energetic photons is striking Venus at about 10^30 per second and the age of the solar system is about 10^17 seconds, estimate the total mass of water that could have been lost from Venus since it formed. Th mass of a water molecule is 18 x 10^-27kg.

Any help will be much appreciated.

Edit: all I have figured thus far is that # of photons striking multiplied by charge of an electron gives the energy transferred to the H20 but how do I figure out how much is needed to dissociate the H20 and in turn how much H20 will be lost because of it?

 

[OlderDan]

You need to take another look at the energy of a photon. Unless you have been given specific information, you will have to make some assumptions about the energy of a typical photon, and how much of its energy can be absorbed by the water (all of it perhaps?) You will then need to know how much energy a water molecule would need to escape the gravity of Venus.

 

[physical1]

Interesting old post. Where to find information on how much energy a "typical" photon holds? Are there non-typical photons?

 

[Borek]

Question asked for "energetic" photons - my bet is that they meant "those able to shoot water molecules from the Venus gravity field" and whole question is a just an exercise in dimensional analysis.

Edit: no, it must be more complicated; unless I did some mistake in my calculations this approach gives absurd result (too much water).

 

[Hao]

By absurd, was it on the order of $$10^{21}$$ kg?

The Earth has $$1.36 * 10^{21}$$ kg of water, so having an answer that is similar or somewhat larger seems to make sense considering that there is hardly any water on Venus - 20ppm in the atmosphere.

This also sets upper bounds, as the water could have been lost a long time ago, but the answer estimates the maximum amount of water Venus could have had when it was first formed to not have any water today.

Rhetorical question: If we fast forward to 1 trillion years in the future (assuming that we can go that far), our answer would be $$10^3$$ larger, but would it be any more or less unreasonable?

On the other hand, the title refers to dissociation rather than ejection of water. It is possible that some fraction would have recombined back into water.

 

[Borek]

Hm, somehow I have managed to miss the result by 10³ and got 10²⁴ kg - comparable to Earth mass. 10²¹ looks much better.