To determine the number of geometrical isomers for the given structure:
Identifying Stereocenters: The given structure contains three stereocenters, which influence the overall geometric configurations.
Counting Geometrical Isomers: The maximum potential geometric isomers can be calculated using the formula:
Total Geometrical Isomers = 2n
where n is the number of stereocenters. In this case:
23 = 8
However, due to symmetry in the molecule, some configurations are equivalent, reducing the number of unique geometrical isomers.
Final Count: Considering the symmetry and equivalent configurations, the total number of unique geometrical isomers for the given structure is 4.
Draw the possible isomers of:
\[ [ \text{Co}(\text{en})_2\text{Cl}_2 ]^+ \]
The incorrect statements regarding geometrical isomerism are:
(A) Propene shows geometrical isomerism.
(B) Trans isomer has identical atoms/groups on the opposite sides of the double bond.
(C) Cis-but-2-ene has higher dipole moment than trans-but-2-ene.
(D) 2-methylbut-2-ene shows two geometrical isomers.
(E) Trans-isomer has lower melting point than cis isomer.
If \[ f(x) = \int \frac{1}{x^{1/4} (1 + x^{1/4})} \, dx, \quad f(0) = -6 \], then f(1) is equal to:
If the system of equations \[ (\lambda - 1)x + (\lambda - 4)y + \lambda z = 5 \] \[ \lambda x + (\lambda - 1)y + (\lambda - 4)z = 7 \] \[ (\lambda + 1)x + (\lambda + 2)y - (\lambda + 2)z = 9 \] has infinitely many solutions, then \( \lambda^2 + \lambda \) is equal to: