Among the lanthanides the one obtained by synthetic method is
(a)Lu
(b)Pm
(c)Pr
(d)Gd

Options

A. Lu
B. Pm
C. Pr
D. Gd

Explanation

To determine which lanthanide is obtained by synthetic methods, we can follow these steps:

### Step 1: Understand the Lanthanides
The lanthanides are a series of 15 chemical elements from lanthanum (La) to lutetium (Lu) in the periodic table, with atomic numbers ranging from 57 to 71.

### Step 2: Identify the Options
The options given are:
- (a) Lu (Lutetium, atomic number 71)
- (b) Pm (Promethium, atomic number 61)
- (c) Pr (Praseodymium, atomic number 59)
- (d) Gd (Gadolinium, atomic number 64)

### Step 3: Research Each Element
- **Lutetium (Lu)**: Naturally occurring, found in minerals.
- **Promethium (Pm)**: Atomic number 61, not found in nature; it is radioactive and can only be produced synthetically.
- **Praseodymium (Pr)**: Naturally occurring, found in minerals.
- **Gadolinium (Gd)**: Naturally occurring, found in minerals.

### Step 4: Conclusion
Among the lanthanides listed, Promethium (Pm) is the only one that is not found in nature and is obtained through synthetic methods. Therefore, the correct answer is:

**(b) Pm (Promethium)**

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