Order the following atoms from smallest to largest, judging from their relative positions in the periodic table: \(\mathrm{Cs}, \mathrm{Fe}, \mathrm{Ti}, \mathrm{Hf}\)

We need to find out where the given elements, \(\mathrm{Cs}\), \(\mathrm{Fe}\), \(\mathrm{Ti}\), and \(\mathrm{Hf}\), are located in the periodic table. - \(\mathrm{Cs}\): Cesium is in Group 1 (Alkali metals) and Period 6. - \(\mathrm{Fe}\): Iron is in Group 8 (Transition metals) and Period 4. - \(\mathrm{Ti}\): Titanium is in Group 4 (Transition metals) and Period 4. - \(\mathrm{Hf}\): Hafnium is in Group 4 (Transition metals) and Period 6.

Keeping in mind that atomic size increases going down a group and decreases going across a period from left to right, comparing the elements in this order will allow us to find the smallest to largest: 1. Compare \(\mathrm{Fe}\) and \(\mathrm{Ti}\): They are both in Period 4, with \(\mathrm{Fe}\) in Group 8 and \(\mathrm{Ti}\) in Group 4. Since atomic size decreases from left to right, \(\mathrm{Ti}\) is larger than \(\mathrm{Fe}\). 2. Compare \(\mathrm{Cs}\) and \(\mathrm{Hf}\): They are both in Period 6, with \(\mathrm{Cs}\) in Group 1 and \(\mathrm{Hf}\) in Group 4. Since atomic size decreases from left to right, \(\mathrm{Cs}\) is larger than \(\mathrm{Hf}\). 3. Compare \(\mathrm{Ti}\) and \(\mathrm{Hf}\): They are both in Group 4, with \(\mathrm{Ti}\) in Period 4 and \(\mathrm{Hf}\) in Period 6. Since atomic size increases going down a group, \(\mathrm{Hf}\) is larger than \(\mathrm{Ti}\). 4. We already know \(\mathrm{Cs}\) is the largest atom among the elements given. Therefore: Cs > Hf > Ti > Fe So, the order of atoms from smallest to largest judging by their positions in the periodic table is: \(\mathrm{Fe} \rightarrow \mathrm{Ti} \rightarrow \mathrm{Hf} \rightarrow \mathrm{Cs}\).