Final answer:
If a researcher uses a liquid twice as dense as mercury in a barometer, the liquid will rise to a height of 380 mm, half the height required for mercury, due to the inversely proportional relationship between the density of the liquid and the height of the column formed under atmospheric pressure.
Step-by-step explanation:
Given that standard atmospheric pressure can support a 760 mm column of mercury, which is 13.6 times denser than water, one can use the ratio of densities to determine the height of a column of a liquid that is twice as dense as mercury. If the density of mercury is represented as Δ, then the liquid in question has a density of 2Δ. Since the hydrostatic pressure is constant for a given atmospheric condition, we can use the inversely proportional relationship between the density of a liquid and the height of the column it forms under a specific pressure.
Therefore, if a column of mercury with density Δ under atmospheric pressure has a height of 760 mm, a liquid of density 2Δ would only need a column that is half as tall to exert the same pressure.
This means the liquid would rise to a height of 380 mm in the researcher's barometer.