Question

Predict the atomic radius, density, and melting point for radioactive radium. $$\begin{array}{cccc}\hline \text { Element } & \text { Atomic Radius } & \text { Density at } 20^{\circ} \mathrm{C} & \text { Melting Point } \\\\\hline \mathrm{Sr} & 0.215 \mathrm{nm} & 2.63 \mathrm{~g} / \mathrm{mL} & 769^{\circ} \mathrm{C} \\\\\mathrm{Ba} & 0.217 \mathrm{nm} & 3.65 \mathrm{~g} / \mathrm{mL} & 725^{\circ} \mathrm{C} \\\\\mathrm{Ra} & (?) \mathrm{nm} & (?) \mathrm{g} / \mathrm{mL} & (?){ }^{\circ} \mathrm{C} \\\\\hline\end{array}$$

Short answer

Ra's atomic radius is about 0.220 nm, density ~5 g/mL, and melting point ~700°C.

Step-by-step solution

Analyze Periodic Table Trends

Radium (Ra) is in Group 2 of the periodic table, also known as the alkaline earth metals. Elements in the same group have similar properties, and trends can be observed going down the group. Atomic radius increases moving down a group due to the addition of electron shells.

Predict Atomic Radius

Given the atomic radii of Strontium (Sr) as 0.215 nm and Barium (Ba) as 0.217 nm, we can predict that Radium (Ra) will have a slightly larger atomic radius than Barium, as it is further down the group. Therefore, we estimate Ra's atomic radius to be approximately 0.220 nm.

Predict Density

The density of alkaline earth metals generally increases down the group, as atomic masses increase more significantly than volumes. With Sr having a density of 2.63 g/mL and Ba having 3.65 g/mL, we can predict Ra will have a slightly higher density than Ba, around 5 g/mL.

Predict Melting Point

The melting points of Group 2 elements generally decrease down the group. Sr has a melting point of 769°C, while Ba is 725°C. Since Ra is further down the group, we can expect it to have a lower melting point than Ba, estimated around 700°C.

Key concepts

Atomic Radius of Alkaline Earth Metals

The atomic radius gives an indication of the size of an atom. It is typically measured as the distance from the nucleus to the outermost electron shell. Understanding trends in atomic radius helps us predict properties of elements that may not be directly observable. In the periodic table, the atomic radius tends to increase as you move down a group. This is because each subsequent element has an additional electron shell, making the atom larger overall. For alkaline earth metals, such as Strontium (Sr), Barium (Ba), and Radium (Ra), this trend means that Radium, being further down the group, has the largest atomic radius. - **Atomic Radius Trend:** Moving down Group 2, the atomic radii increase. - **Example:** Sr's atomic radius is 0.215 nm, Ba's is slightly larger at 0.217 nm. Thus, Ra is predicted to be about 0.220 nm. The increase in atomic radius from Sr to Ra is consistent with the addition of electron shells as we move down the group.

Density Prediction for Radium

Density is defined as mass per unit volume. For metals, density increases as you move down a group in the periodic table. This increase is due to the increase in atomic mass being greater than the increase in atomic volume. In the case of alkaline earth metals, while they all have similar metallic structures, the atomic mass significantly influences their density. Given the densities of Strontium (Sr) and Barium (Ba) are 2.63 g/mL and 3.65 g/mL respectively, we can expect Radium (Ra), further down the group, to have a higher density. - **Density Trend:** As you go down Group 2, density typically increases. - **Example:** With the progression from Sr to Ba, we see an increase in density. Consequently, Ra is expected to have an even higher density, predicted around 5 g/mL. This prediction aligns perfectly with the periodic trend for density of heavier alkaline earth metals.

Melting Point Trends in Alkaline Earth Metals

Melting points of the elements are also affected by the periodic trends. Typically, for Group 2 elements, the melting points decrease as you move down the group. This is somewhat opposite to trends seen in atomic radius and density. The decrease in melting points down the group can be attributed to the weakening of metallic bonds, as the atomic size increases. The attractions holding the atoms in a solid state become weaker, lowering the energy required to transition to a liquid state. - **Melting Point Trend:** Generally decreases down Group 2. - **Example:** Sr and Ba have melting points of 769°C and 725°C respectively. Radium, being further down the group, is expected to have a lower melting point around 700°C. Understanding these trends helps predict melting points for elements like Ra, where direct measurements might be challenging due to properties like radioactivity.