GATE CY 2012 Question Paper (12-Feb-2012) (Shift-2)

The angular part of the wavefunction for the electron in a hydrogen atom is proportional to ${\sin }^2\theta \cos \theta e^{2i\varphi }$. The values of the azimuthal quantum number ($l$) and the magnetic quantum number ($m$) are, respectively

Let ${\varphi }_x^C$ and ${\varphi }_z^C$ denote the wavefunctions of the $2p_x$ and $2p_z$ orbitals of carbon, respectively, and ${\varphi }_x^O$ and ${\varphi }_z^O$ represent the wavefunctions of the $2p_x$ and $2p_y$ orbitals of oxygen, respectively. If $c_1$ and $c_2$ are constants used in linear combinations and the CO molecule is oriented along the $z$ axis, then, according to molecular orbital theory, the $\pi$ -bonding molecular orbital has a wavefunction given by

The bond that gives the most intense band in the infrared spectrum for its stretching vibration is

If $x_A$ and $x_B$ are the respective mole fractions of A and B in an ideal solution of the two and $T_A$, $T_B$, $T$ are the fusion temperatures of pure A, pure B and the ideal solution respectively, then

For a reaction involving two steps given below
First step: G $\rightleftharpoons$ 2H
Second step: G + H $\to$ P
assume that the first step attains equilibrium rapidly. The rate of formation of P is proportional to