How effective are Mountain Observatories?

Depends on exactly what you want the telescope to do, so here's a rundown.

For X-Ray, Gamma Ray, and most UV and Infrared telescopes, mountain observatories simply don't work. Even on very high mountains, those types of radiation still don't get through.

For radio telescopes, the height doesn't really matter, and the size of the telescope is more important, so real radio telescopes are built at sea level, where it's easier to build and maintain a bigger system.

Optical observatories are the ones put on mountains. They measure visible light, and do a fairly decent job for most things (that's what most astronomers have to live with anyway). There are also systems like Adaptive Optics, which can deal with most of the problems caused by the atmosphere (although they aren't perfect).

Orbiting telescopes above the atmosphere are far more effective than those on the ground, as they have no atmospheric distortion. Their main disadvantage is their much greater cost and the fact that they can't be as big as ground-based ones, but even so they are definitely worth it.

a million. F 2. F 3. No clue reason i don't get into Chromatic aberration nor do I care to. nuf pronounced 4. No clue reason i do no longer understand what a interferometer is I merely understand astronomy. 5. F 6. F (with the aid of far Radio Telescopes are the biggest) 7. No clue reason it style of sounds like new scopes of all varieties are equipped on a daily basis.

In the mountains you're above most of the cloud layers and the smog. The brightest stars I've ever seen were in the mountains at night.

it depends on the elevation of the mountain and the technology that the observatory is using ( ex. the size of their telescope , etcs. )

The higher, the better. You want to get rid of the most distorting atmosphere between space and your telescope. Speaking about light telescopes, of course. Radio telescopes can be built on flat ground.