Paper: CSIR-NET December 2011 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Character Tables · Marks: 2 · Difficulty: Hard
The character table for the $\mathrm{D_4}$ point group is provided below:
$\mathrm{D_3}$
E
$2\mathrm{C_3}$
3C
$\mathrm{A_1}$
1
1
1
$x^2+y^2, z^2$
$\mathrm{A_2}$
1
1
-1
$z, R_z$
E
2
-1
0
$(x,y),(R_x,R_y)$
$(x^2-y^2, xy),(xz,yz)$
For this point group, the correct statement among the following is:
(a)it is possible to have a totally symmetric normal mode of vibration which is IR-active
(b)all IR-active normal modes are necessarily Raman inactive
(c)all Raman-active normal modes are necessarily IR-active
(d)it is possible to have a pair of IR-active normal modes that are degenerate.
Answer
Answer: D ✓ checked by 4AB · confidence high
Explanation
In D₄, z is A₂ and (x, y) is E, so A₁ is never IR-active (a false), A₁ is Raman-only (c false), E is both IR and Raman active (b false) and the degenerate E modes are IR-active (d true).