If the electronic structure of oxygen atom is written as $1{\mathrm{s}}^2, 2{\mathrm{s}}^2$  it would violate:

1.  Hund's rule

2.  Paulis exclusion principle

3.  Both Hund's and Pauli's principles

4.  None of the above

The correct order of the total number of nodes of atomic orbitals is: 

1.  4f > 6s > 5d

2.  6s > 5d > 4f

3.  4f > 5d > 6s

4.  5d > 4f > 6s

Correct statement among the following is: 

1.  Number of angular nodes = n - l - 1

2.  Number of radial nodes = l

3.  Total number of nodes = n -1

4.  All of the above

Which orbital has the maximum number of total nodes?
1.  5s

2.  5p

3.  5d

4.  All have the same number of nodes.

Orbitals having two spherical nodes are: 

The correct Schrodinger's wave equation for a electron with total energy E and potential energy V is given by

1.  $\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{x}}^2}+\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{y}}^2}+\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{z}}^2}+\frac{8{\mathrm{\pi }}^2}{{\mathrm{mh}}^2}\left(\mathrm{E}-\mathrm{V}\right) \mathrm{\psi }=0$

2.  $\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{x}}^2}+\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{y}}^2}+\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{z}}^2}+\frac{8\mathrm{\pi m}}{{\mathrm{h}}^2}\left(\mathrm{E}-\mathrm{V}\right) \mathrm{\psi }=0$

3.  $\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{x}}^2}+\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{y}}^2}+\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{z}}^2}+\frac{8{\mathrm{\pi }}^2\mathrm{m}}{{\mathrm{h}}^2}\left(\mathrm{E}-\mathrm{V}\right) \mathrm{\psi }=0$

4.  None of the above.

The development of the wave mechanical model of the atom is based on which of the following concepts?

1.  De-Broglie concept of the dual nature of the electron.

2.  Heisenberg uncertainty principle.

3.  Schrodinger's principle

4.  All of the above

${\mathrm{\psi }}^2\left(\mathrm{r}, \mathrm{\theta }, \mathrm{\varphi }\right)$ represents: (for Schrodinger wave mechanical model)

1.  Amplitude of electron wave

2.  Probability density of electron

3.  Total probability of finding electron around nucleus

4.  Orbit

Radial amplitude of electron wave can be represented by

1.  $\mathrm{R}\left(\mathrm{r}\right)$

2.  ${\mathrm{R}}^2\left(\mathrm{r}\right)$

3.  $4{\mathrm{\pi r}}^2$

4.  $4{\mathrm{\pi r}}^2{\mathrm{R}}^2\left(\mathrm{r}\right)$

The Schrodinger wave equation for the hydrogen atom is \(\psi_{2 s}=\frac{1}{4 \sqrt{2 \pi}}\left(\frac{1}{a_0}\right)^{3 / 2}\left(2-\frac{\mathrm{r}}{\mathrm{a}_0}\right) \mathrm{e}^{-\mathrm{r} / \mathrm{a}_0}\) where ${\mathrm{a}}_0$ is Bohr's radius. If the radial node in 2s be at ${\mathrm{r}}_0$, then ${\mathrm{r}}_0$ would be equal to:

1.  $\frac{{\mathrm{a}}_0}{2}$

2.  $2{\mathrm{a}}_0$

3.  $\sqrt{2}{\mathrm{a}}_0$

4.  $\frac{{\mathrm{a}}_0}{\sqrt{2}}$