It is not possible to measure the atomic radius precisely since the electron cloud surrounding the atom does not have a sharp boundary. One practical approach to estimate the size of an atom of a non-metallic element is to measure the distance between two atoms when they are bound together by a single bond in a covalent molecule and then dividing by two. For metals we define the term "metallic radius" which is taken as half the inter nuclear distance separating the metal cores in the metallic crystal. Then van der waal's radius represents the over all size of the atoms which includes its valence shell in a non bonded situation. It is the half of the distance between two similar atoms in separate molecules in a solid. The atomic radius decreases across a period and increases down the group. Same trends are observed in case of ionic radius. Ionic radius of the species having same number of electrons depends on the number of protons in their nuclei. Sometimes, atomic and ionic radii give unexpected trends due to poor shielding of nuclear charge by `d`-and `f-`orbital electrons.
Now answer the following three questions:
Which of the following relations is correct, if considered for the same element.

Options

A. `r_("vandewaal") gt r_("Covalent") gt r_("Metallic")`
B. `r_("Covalent") gt r_("Metallic") gt r_("Vanderwaal")`
C. `r_("Vanderwaal") gt r_("Metallic") gt r_("Covalent")`
D. `r_("Metallic") gt r_("Covalent") gt r_("Vanderwaal")`

Answer

To answer the question regarding the correct relationship between atomic and ionic radii for the same element, we can analyze the trends and definitions provided in the context of atomic structure and periodicity.

### Step-by-Step Solution:

1. **Understanding Atomic Radius**: The atomic radius is defined as the distance from the nucleus to the outermost shell of electrons. It is not a fixed value due to the electron cloud's nature, but it can be estimated through various methods, such as measuring bond lengths in covalent compounds.

2. **Understanding Ionic Radius**: The ionic radius refers to the size of an ion in a crystal lattice. For ions of the same element, the ionic radius can vary depending on whether the ion is positively charged (cation) or negatively charged (anion). Cations are generally smaller than their neutral atoms because they lose electrons, resulting in a stronger effective nuclear charge per electron. Anions are larger because they gain electrons, which increases electron-electron repulsion.

3. **Trends Across a Period**: As we move from left to right across a period in the periodic table, the atomic radius decreases due to the increasing nuclear charge, which pulls the electron cloud closer to the nucleus. This trend also applies to ionic radii, where cations decrease in size across a period.

4. **Trends Down a Group**: As we move down a group, the atomic radius increases because additional electron shells are added, which outweighs the effect of increasing nuclear charge. The same trend is observed for ionic radii, where both cations and anions increase in size down a group.

5. **Comparison of Atomic and Ionic Radii**: For the same element, the ionic radius of cations will always be smaller than the atomic radius of the neutral atom, while the ionic radius of anions will be larger than the atomic radius. This is due to the loss or gain of electrons affecting the electron cloud's size relative to the nucleus.

### Conclusion:
The correct relationship for the same element is:
- **Cation Radius < Atomic Radius < Anion Radius**