Answer :

To determine which element has the largest atomic radius among Thallium (TI), Chlorine (CI), Arsenic (As), and Francium (Fr), we need to consider the position of each element in the periodic table.

1. Thallium (TI):
- Thallium is located in Group 13 and Period 6 of the periodic table. Elements in this region tend to have larger atomic radii compared to those higher up in the same group due to the addition of more electron shells.

2. Chlorine (CI):
- Chlorine is located in Group 17 and Period 3. Elements in Group 17 tend to be non-metals with smaller atomic radii because they tend to gain electrons to form negative ions and have a higher nuclear charge which pulls electrons closer.

3. Arsenic (As):
- Arsenic is found in Group 15 and Period 4. While it has a larger atomic radius than Chlorine because it is lower on the periodic table, it generally has a smaller atomic radius than elements in Group 13 of the same period.

4. Francium (Fr):
- Francium is in Group 1 and Period 7. Elements in Group 1 are alkali metals and are known for having large atomic radii. Francium, being at the bottom of Group 1, will have the largest atomic radius among the given elements due to having the most electron shells and the least effective nuclear charge at holding the outermost electrons close to the nucleus.

Considering the periodic trends and the positions of these elements:
- Atomic radius increases down a group as more electron shells are added.
- Atomic radius decreases across a period from left to right as effective nuclear charge increases.

Given these trends, Francium (Fr) will have the largest atomic radius among the given options.

Thus, the element with the largest atomic radius is:

Francium (Fr).