The f-block elements are those in which the differentiating electron enters the (n-2)f orbital. There are two series of f-block elements corresponding to filling of 4f and 5f-orbitals called lanthanides and actinides respectively. They show different oxidation states depending upon the stability of `f^0, f^7`and `f^14` configurations, though the principal oxidation state is +3. There is a regular decrease in size of lanthanide ions with increase in atomic number and it is known as lanthanide contraction. As a result of this, the basic character of oxides and hydroxides decreases from first element (La) to last element (Lu). All the actinides are radioactive and therefore, it is difficult to study their chemical nature.
Which of the following statements is not true ?

Options

A. ` La (OH)_3` is more basic than `Lu(OH)_3`
B. All f-block elements are radioactive in nature
C. The principal oxidation state of lanthanides is +3
D. The size of trivalent lanthanide ions decrease in 4f block series.

Explanation

To determine which statement is not true regarding the f-block elements, we will analyze the provided statements one by one.

### Step 1: Understand the f-block elements
The f-block elements consist of two series: lanthanides (4f) and actinides (5f). The differentiating electrons enter the (n-2)f orbitals, and the principal oxidation state for lanthanides is typically +3.

### Step 2: Analyze the statements
1. **Statement A**: "La(OH)₃ is more basic than Lu(OH)₃."
- As we move from La to Lu in the lanthanide series, the size of the ions decreases due to lanthanide contraction. A smaller ionic size leads to a higher effective nuclear charge, which in turn decreases the basic character of the hydroxides. Therefore, La(OH)₃ is indeed more basic than Lu(OH)₃. This statement is true.

2. **Statement B**: "All f-block elements are radioactive in nature."
- This statement is incorrect. While all actinides are radioactive, not all lanthanides are. Lanthanides (atomic numbers 57 to 71) include elements like La, Ce, and Pr, which are stable and not radioactive. Therefore, this statement is not true.

3. **Statement C**: "The principal oxidation state of lanthanides is +3."
- This statement is true. The most common oxidation state for lanthanides is indeed +3.

4. **Statement D**: "The size of trivalent lanthanide ions decreases in the 4f block series."
- This statement is also true. The ionic size of trivalent lanthanide ions decreases as we move from La to Lu due to lanthanide contraction.

### Conclusion
The statement that is not true is **Statement B**: "All f-block elements are radioactive in nature."

### Final Answer
**The statement that is not true is B: "All f-block elements are radioactive in nature."**

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