How many geometrical isomers are possible in the following two alkenes?
(i) `CH_(3)-CH=CH-CH=CH-CH_(3)`
`CH_(3)-CH=CH-CH=CH-Cl`

Options

A. 4 and 4
B. 4 and 3
C. 3 and 3
D. 3 and 4

Explanation

To determine the number of geometrical isomers for the given alkenes, we will analyze each compound step by step.

### Step 1: Analyze the first alkene `CH₃-CH=CH-CH=CH-CH₃`

1. **Identify the double bonds**: The first alkene has two double bonds (C=C).
2. **Identify sp² hybridized carbons**: Each carbon involved in a double bond is sp² hybridized. Here, we have 4 sp² hybridized carbons.
3. **Check for identical end groups**: The end groups of this alkene are both methyl groups (CH₃), which are identical.

**Formula for geometrical isomers**: When the end groups are similar, the formula to find the number of geometrical isomers is:
\[ \text{Number of isomers} = 2^n \]
where \( n \) is the number of double bonds.

- Here, \( n = 2 \) (two double bonds).
- Thus, the number of geometrical isomers is:
\[ 2^2 = 4 \]

### Step 2: Analyze the second alkene `CH₃-CH=CH-CH=CH-Cl`

1. **Identify the double bonds**: The second alkene also has two double bonds (C=C).
2. **Identify sp² hybridized carbons**: Again, we have 4 sp² hybridized carbons.
3. **Check for identical end groups**: The end groups of this alkene are CH₃ (methyl) and Cl (chlorine), which are different.

**Formula for geometrical isomers**: When the end groups are different, the formula to find the number of geometrical isomers is:
\[ \text{Number of isomers} = 2^{p-1} + 2^{n-1} \]
where \( p \) is the number of pairs of double bonds and \( n \) is the total number of double bonds.

- Since there are 2 double bonds (even), we calculate \( p \) as:
\[ p = \frac{n}{2} = \frac{2}{2} = 1 \]
- Now, substituting \( p \) and \( n \) into the formula:
\[ \text{Number of isomers} = 2^{1-1} + 2^{2-1} = 2^0 + 2^1 = 1 + 2 = 3 \]

### Summary of Results:
- For the first alkene `CH₃-CH=CH-CH=CH-CH₃`: **4 geometrical isomers**
- For the second alkene `CH₃-CH=CH-CH=CH-Cl`: **3 geometrical isomers**

### Final Answer:
- **4 geometrical isomers for the first alkene**
- **3 geometrical isomers for the second alkene**

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