Determining the Level of Mercury in U shaped tube

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To determine the height L of mercury in a U-shaped tube, the relationship between the air pressure and the mercury pressure must be established. Initially, the tube contains air at 293K and 1 atm, which compresses as mercury is added. The pressure of the air must equal the pressure exerted by the mercury column, calculated using the formula P = P0 + pgd. The conversion of atmospheric pressure to mmHg is necessary, as 1 atm equals 760 mmHg. Understanding these pressure relationships will lead to the solution for L.
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Homework Statement



A u shaped tube has a total length of 1 m, it is initially filled with air at 293K 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

The tube is open at one end, closed at the other

Homework Equations


We have PV=NRT, P=P_0 +pgd


The Attempt at a Solution


Obviously I have to relate the air levels to that of mercury, as well as relating pressures, 1 atm = 760 mmHG so there is that, but its no longer at 1 atm. Someone want to give me a hint here? I am not looking for the answer just some insight. Everything I can think of deals with the area or the density
 
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The air pressure must equal the pressure of the mercury at its surface in contact with the air. The pressure of the mercury will be the weight of the column of mercury on the other side of the tube, above that contact surface, divided by the surface area.
 

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