Where are Obi-Wan Kenobi's and Qui-gon Jinn's lightsabers?

Question

In Star Wars Episode 1: The Phantom Menace, when Darth Maul kills Qui-Gon Jinn, Obi-Wan Kenobi starts a saber duel with Darth Maul, and Darth Maul uses a force push on Obi-Wan Kenobi. Obi-Wan hangs on that deep and dark big pipe. Then, Darth Maul kicks Kenobi's lightsaber into that hole. After that, Obi-Wan uses Qui-Gon Jinn's lightsaber to defeat Darth maul.

My questions are:

1. Where Is Obi-Wan's lightsaber? Does he build a new one or retrieve it from somewhere like from bottom of that big pipe or etc.?
2. What about Qui-Gon Jinn's lightsaber? Where is it?

Answer 1

The answer I've provided is based on Wookieepedia articles (linked in text) and my recollection of the G-canon material.

1.

This wiki article states that Obi-wan constructs a new Lightsaber after his first one is kicked down the melting pit (the big pipe you mention), which suggests that he does not recover his original lightsaber.

As such, my answer to this is that he built a new one and that the first one is left at the bottom of the pit.

2.

As for Qui-gon Jinn's lightsaber, it was used briefly by Obi-Wan Kenobi following the events of The Phantom Menace, but only until he had time and opportunity to construct a new one. After that, its fate is unknown.

Note: There has been some speculation that Kenobi brought Qui-Gon Jinn's lightsaber with him to Tatooine, where it remained until Luke Skywalker came back to construct his second lightsaber, following the events of Empire Strikes Back. This article, however, disputes this.

Answer 2

That "big pipe" was in fact a melting pit. The implication is that in the centre of the pit...erm...stuff gets melted. Since Obi-Wan's original lightsaber went into the pit, we can assume it was destroyed.

The struggle took them around the edge of the melting pit and into the nooks and alcoves beyond, into shadowed recesses and around smoky pillars and pipe housings. Twice, Obi-Wan went down, losing his footing on the smooth flooring of the melting pit’s rim. Once, Darth Maul hammered at him with such determination that he scorched the young Jedi’s tunic, shoulder to waist, and it was only by countering with an upthrust counterstrike to the other’s midsection and by rolling quickly away and back to his feet that Obi-Wan was able to escape. - _{^{Phantom Menace - Official Novelisation}}

Sometime before the start of Attack of the Clones (some 10+ years later), Obi-Wan stopped using Qui-Gon's lightsaber and constructed a second lightsaber of his own, identical to the first.

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As to where the real prop went, Liam Neeson apparently has it.

"Before we started shooting, George showed up with a huge gilded box. In it were lightsabers, and he asked me to pick one. I chose one, and he said, 'That's yours now.' It was quite a moment. And I did get to keep it — it was mounted for me at the end of the film. I was thrilled."