Question

question: how can you tell if a crown is made of solid gold? 1. think about it: gold is one of the densest substances known, with a density of 19.3 g/cm³. if the gold in the crown was mixed with a less - valuable metal like bronze or copper, how would that affect its density? 2. observe: drag each of the crowns into the liquid. based on what you see, which crown do you think is densest? explain why you think so. 3. measure: find the mass, volume, and density of each of the three crowns. 4. draw conclusions: which of the three crowns was made of gold? explain.

Explanation:

Step1: Recall density formula

Density $
ho=\frac{m}{V}$, where $m$ is mass and $V$ is volume.

Step2: Determine gold - density comparison

Gold has a density of $
ho_{gold}=19.3\ g/cm^{3}$. If a crown is mixed with a less - dense metal like bronze or copper, its overall density $
ho_{mix}$ will be less than $19.3\ g/cm^{3}$ because density is mass per unit volume and adding a less - dense metal decreases the average density.

Step3: Measuring mass and volume

To find the density of each crown, measure its mass $m$ using a balance and its volume $V$ using water displacement (immerse the crown in a graduated cylinder filled with water and measure the volume of water displaced). Then calculate $
ho=\frac{m}{V}$ for each crown.

Step4: Compare with gold density

The crown with a density closest to $19.3\ g/cm^{3}$ is most likely made of solid gold. If the density is significantly less, it is likely mixed with other metals.

Answer:

Measure the mass and volume of each crown, calculate their densities using the formula $
ho = \frac{m}{V}$, and compare the calculated densities with the known density of gold ($19.3\ g/cm^{3}$). The crown with a density closest to $19.3\ g/cm^{3}$ is most likely made of solid gold.