Question

Which of the following is/are correctly matched?

Compound	Number of geometric isomer
a. $C{H}_3-CH=CH-CH=CH-C_2{H}_5$	4
b. $C{H}_3-(CH=CH{)}_4-C{H}_3$	2
c. $H_{2}C=CH-CH=C{H}_2$	$2^4+2^1=10$
d. $C{H}_3-(CH=CH{)}_5-C{H}_3$	$2^4+2^2=20$

• A. Only a
• B. b & c
• C. a & d
• D. All of the above

Answer 1

The correct option is C a & d

$\text{When a compound has 'n' double bonds and ends of a polyene are different (unsymmmetrical)}$

The number of geometrical isomers = $2^n$
a) n=2
number of geometrical isomers = $2^n=2^2=4$
a) is correctly matched.

$\text{When the ends of polyene are same.}$

$\text{Case I}:$

When number of double bonds ($=n$) is even then the number of geometrical isomers = $2^{n-1}+2^{\left[\right(n/2)-1]}$

b) n=4,even
Number of geometrical isomers = $2^{n-1}+2^{\left[\right(n/2)-1]}=2^3+2^1=8+2=10$
b) is incorrect.

c) n=2,even
Number of geometrical isomers = $2^{n-1}+2^{\left[\right(n/2)-1]}=2^1+2^0=2$
c) is incorrectly matched

$\text{Case II}:$

When number of double bonds ($=n$) is odd. Number of geometrical isomers = $2^{n-1}+2^{(n-1)/2}$

d) Here n=5

Number of geometrical isomers = $2^{n-1}+2^{(n-1)/2}=2^{5-1}+2^{(5-1)/2}=2^4+2^2=16+4=20$
d) is also correctly matched.

a & d are correctly matched.

Option C is correct.