Answer :

To determine which of the elements Germanium (Ge), Potassium (K), Gallium (Ga), or Calcium (Ca) has the largest atomic radius, we need to understand trends in the periodic table.

1. Periodic Trends:
- The atomic radius tends to increase as you move down a group in the periodic table because each successive element has an additional electron shell.
- The atomic radius tends to decrease as you move from left to right across a period because the increasing positive charge in the nucleus pulls the electrons closer.

2. Element Placement:
- Potassium (K) is in Group 1 and Period 4.
- Calcium (Ca) is in Group 2 and Period 4.
- Gallium (Ga) is in Group 13 and Period 4.
- Germanium (Ge) is in Group 14 and Period 4.

3. Analysis based on Trends:
- Within the same period (Period 4 in this case), atomic radius decreases from left to right.
- Therefore, the atomic radius should be largest for the element furthest to the left (Potassium) and smallest for the element furthest to the right (Germanium).

4. Comparing the Elements:
- Potassium (K) is furthest to the left in Period 4. Thus, it should have the largest atomic radius.
- Calcium (Ca) comes next, followed by Gallium (Ga) and Germanium (Ge).

Based on the periodic trends and the positions of these elements in Period 4, the element with the largest atomic radius is Potassium (K).