Question

To determine the age of archaeological sediments using Optically Stimulated Luminescence (OSL), researchers extract coarse-grain quartz under strictly controlled conditions to prevent resetting the geological signal. Under dim red light, the raw sediment is first sieved to isolate grains between $90$ and $250$ micrometers. Subsequently, the isolated fraction is treated with hydrochloric acid ($\\text{HCl}$) to dissolve carbonates, which could otherwise interfere with subsequent chemical treatments. Once the effervescence ceases, the sample is washed prior to being treated with hydrogen peroxide ($\\text{H}_2\\text{O}_2$) to remove organic matter. Crucially, the remaining minerals are then subjected to a dense liquid separation using sodium polytungstate at a specific gravity of $2.62\\text{ g/cm}^3$ to float off potassium feldspars, which exhibit unwanted luminescence signals. Finally, the remaining heavy fraction is etched with concentrated hydrofluoric acid ($\\text{HF}$) for $40$ minutes. This $\\text{HF}$ etching serves a dual purpose: it dissolves any remaining feldspars and simultaneously etches away the alpha-irradiated outer shell of the quartz grains, leaving pure quartz cores ready for measurement.

Based on the passage, if a researcher omits the dense liquid separation step using sodium polytungstate, which of the following is the most likely consequence for the final quartz sample?