`CH_(3)CH=CH-CH=CH-CH_(2)CHOHCH_(3)`
How many isomers (geometrical and optical) are possible for the above - mentioned compound?

Options

A. 2
B. 4
C. 6
D. 8

Answer

To determine the number of isomers (both geometrical and optical) for the compound `CH₃CH=CH-CH=CH-CH₂CHOHCH₃`, we will follow these steps:

### Step 1: Identify the structure of the compound
The compound can be represented as follows:
- It has a chain of carbon atoms with two double bonds (C=C).
- The structure can be depicted as:
```
CH₃-CH=CH-CH=CH-CH₂-CHOH-CH₃
```
- This compound contains a total of 8 carbon atoms.

### Step 2: Identify the presence of chiral centers
A chiral center is a carbon atom that has four different groups attached to it.
- In the given compound, we need to analyze each carbon atom to find chiral centers.
- The last carbon (attached to -OH) is a chiral center because it has four different groups:
1. -OH
2. -CH₃
3. -H
4. -CH₂-CH=CH-CH=CH-CH₃ (the rest of the chain)

- The other carbons do not have four different groups attached, so they are not chiral.

### Step 3: Count the number of chiral centers
From our analysis, we find that there is **1 chiral center** in the compound.

### Step 4: Calculate optical isomers
The number of optical isomers can be calculated using the formula:
\[ \text{Number of optical isomers} = 2^n \]
where \( n \) is the number of chiral centers.
- Here, \( n = 1 \), so:
\[ \text{Number of optical isomers} = 2^1 = 2 \]

### Step 5: Identify geometrical isomers
Geometrical isomers arise from the presence of double bonds. Each double bond can exhibit cis/trans isomerism.
- The compound has **2 double bonds** (C=C).
- For each double bond, we can have:
- For the first double bond (between C2 and C3), it can be either cis or trans.
- For the second double bond (between C4 and C5), it can also be either cis or trans.

### Step 6: Count the geometrical isomers
For 2 double bonds, the combinations of cis/trans configurations can be calculated as follows:
- For the first double bond (2 options: cis or trans)
- For the second double bond (2 options: cis or trans)

Thus, the total number of geometrical isomers is:
\[ 2 \times 2 = 4 \]

### Step 7: Combine optical and geometrical isomers
Now, we combine the optical and geometrical isomers:
- We have **2 optical isomers** for each of the **4 geometrical configurations**. Therefore, the total number of isomers is:
\[ \text{Total isomers} = 4 \text{ (geometrical)} \times 2 \text{ (optical)} = 8 \]

### Final Answer
The total number of isomers (geometrical and optical) for the compound `CH₃CH=CH-CH=CH-CH₂CHOHCH₃` is **8**.

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