Homework Help: Finding the Length of mercry

1. The problem statement, all variables and given/known data

Au shaped tube has a total length of 1 m, it is initially filled with air at 20* C and 1 atm, mercury is poured in without letting air escape, compressing the air. This continues until the mercury is filled to a level L, how long is L

2. Relevant equations

Im guessing PV=NRT,
It seems like it should involve the density of HG but its not given, nor is the volume


3. The attempt at a solution

I don't even know where to start, It seems like the final pressure is needed, Any suggestions?

 

I'm still missing something, what does that lead to? Is there a formula Im just not seeing, W/E or ....

 

I don't want to appear dense( no pun intended) but I still don't get it. None of the equations I see are in terms of L, only pressure, velocity or area. I can't see how the youngs modulus would have anything to do with it

 

Does it involve the pressure of mercury as 1 atm is 760 mm HG?