How much ozone would it take to block solar radiation on Mars if chambered in double panned glass or material? Said $O_3$ would break down from the UV. Would applied electricity on $O$ and $O_2$ make $O_3$ again? Glass weighs to much and is not an option unless it is made on Mars. I propose gas because it doesn't brake down like UV film can.
If we have $O_2$ lighted with UV, we have actually many reactions working together:
- $O_2 + \gamma \rightarrow 2O$
- $O_2 + O \rightarrow O_3$
- $O_3 + \gamma \rightarrow O_2 + O$
- $O + O_3 \rightarrow 2 O_2$
- $O_3 + O_3 \rightarrow 3O_2$
- $O + O \rightarrow O_2$
(1) produces nascent oxygen. This is slow, and its speed depends on the UV concentration.
(2) builds ozone from nascent oxygen. This is fast.
(3) means the decay of ozone to normal oxygen and nascent oxygen. This can be done very easily with UV light (it has a very big cross-section).
(4), (5) and (6) results the decay of ozone (or nascent oxygen) back to normal oxygen. All of them require that multiple $O$ or $O_3$ molecules need to meet. Thus, it can happen quickly only if there is a high partial ozone pressure.
The net result is that if you light $O_2$ with UV, you get an equilibrial concentration of $O$ and $O_3$ as well. If start with all of ozone, or without a single ozone molecula, the ozone concentration will decay because (4)-(6), or it will be built up because (1), until it reaches this equilibrial concentration. This equilibric concentration will depend on the UV intensity.
(2) and (3) doesn't affect.
Without it, the $O_3$ and $O + O_2$ states will only step into eachother, meanwhile they will eat up a lot of UV radiation. But it can work only if there is a lot of $O_2$ as well.
On the Earth, even in the ionosphere, the ozone concentration is very low: it is roughly 1:100000, and it is between roughly 20 and 30 km. (There are big differences here, for example there is far lesser ozone on the south pole.)
A quick calculation: the pressure of the air decreases to half with around every 5 km elevation. Thus, at 20km high, the pressure is around 1/16 atm. On 30km, it is around 1/64 atm. Calculating with a mean of 1/32, and 10km high, we can compress it to 1atm and 300m height. This calculation is un-exact, but there is no magnitudal differences.
Thus, we would need around a 300m high layer of pure oxygen to get the same UV defense as we have on the Earth.
Remark: a single glass window has a better UV defense as this ozone layer would have, this is why light-skinned people don't get tanned or burned behind them.
Thus, the best UV defense of this biodom would be if it would have simply glass walls. Beside that, there is no ozone layer needed.