Select the correct graphical representation :

Options

A.
B.
C.
D.

Answer

To solve the question regarding the correct graphical representation of the relationship between ionic radii and atomic number for lanthanides, we can follow these steps:

### Step 1: Identify the Elements
The lanthanides series includes the following elements:
- Lanthanum (La)
- Cerium (Ce)
- Praseodymium (Pr)
- Neodymium (Nd)
- Promethium (Pm)
- Samarium (Sm)
- Europium (Eu)
- Gadolinium (Gd)
- Terbium (Tb)
- Dysprosium (Dy)
- Holmium (Ho)
- Erbium (Er)
- Thulium (Tm)
- Ytterbium (Yb)
- Lutetium (Lu)

### Step 2: Understand the Trend
As we move from lanthanum (atomic number 57) to lutetium (atomic number 71) in the lanthanide series:
- The atomic number increases.
- The ionic radii generally decrease due to the increase in effective nuclear charge.

### Step 3: Plot the Graph
On a graph where the x-axis represents the atomic number and the y-axis represents the ionic radii:
- As the atomic number increases from 57 to 71, the ionic radii should show a downward trend.
- This means the graph will slope downwards from left to right.

### Step 4: Select the Correct Graph
Among the provided options, the graph that shows a decreasing trend (downward slope) as the atomic number increases will be the correct representation. According to the video transcript, the first option is the correct one.

### Final Answer
The correct graphical representation is **Option 1**, which shows a downward trend in ionic radii as the atomic number increases for the lanthanides.

---