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

1.  $\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{x}}^2}+\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{y}}^2}+\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{z}}^2}+\frac{8{\mathrm{\pi }}^2}{{\mathrm{mh}}^2}\left(\mathrm{E}-\mathrm{V}\right)<mspace\; width="1em"></mspace>\mathrm{\psi }=0$

2.  $\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{x}}^2}+\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{y}}^2}+\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{z}}^2}+\frac{8\mathrm{\pi m}}{{\mathrm{h}}^2}\left(\mathrm{E}-\mathrm{V}\right)<mspace\; width="1em"></mspace>\mathrm{\psi }=0$

3.  $\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{x}}^2}+\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{y}}^2}+\frac{{\partial }^2\mathrm{\psi }}{\partial {\mathrm{z}}^2}+\frac{8{\mathrm{\pi }}^2\mathrm{m}}{{\mathrm{h}}^2}\left(\mathrm{E}-\mathrm{V}\right)<mspace\; width="1em"></mspace>\mathrm{\psi }=0$

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

${\mathrm{\psi }}^2\left(\mathrm{r},<mspace\; width="1em"></mspace>\mathrm{\theta },<mspace\; width="1em"></mspace>\mathrm{\varphi }\right)$ 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.  $\frac{{\mathrm{a}}_0}{\sqrt{2}}$

The Schrodinger wave equation for hydrogen atom is $\mathrm{\psi }\left(\mathrm{radial}\right)=\frac{1}{16\sqrt{4}}{\left(\frac{\mathrm{Z}}{{\mathrm{a}}_0}\right)}^{3/2}<mspace\; width="1em"></mspace>\left[\left(\mathrm{\sigma }-1\right)<mspace\; width="1em"></mspace>\left({\mathrm{\sigma }}^2-8\mathrm{\sigma }+12\right)\right]{\mathrm{e}}^{-\mathrm{\sigma }/2}$ where ${\mathrm{a}}_0$ and Z are the constant in which answer can be expressed and $\mathrm{\sigma }=\frac{2\mathrm{Zr}}{{\mathrm{a}}_0}$ minimum and maximum position of radial nodes from nucleus are ........ respectively.

1.  $\frac{{\mathrm{a}}_0}{\mathrm{Z}},<mspace\; width="1em"></mspace>\frac{3{\mathrm{a}}_0}{\mathrm{Z}}$

2. $\frac{{\mathrm{a}}_0}{2\mathrm{Z}},<mspace\; width="1em"></mspace>\frac{{\mathrm{a}}_0}{\mathrm{Z}}$

3.  $\frac{{\mathrm{a}}_0}{2\mathrm{Z}},<mspace\; width="1em"></mspace>\frac{3{\mathrm{a}}_0}{\mathrm{Z}}$

4.  $\frac{{\mathrm{a}}_0}{2\mathrm{Z}},<mspace\; width="1em"></mspace>\frac{4{\mathrm{a}}_0}{\mathrm{Z}}$

Isodiaphers among the following options is :

1.  ${}_6{}^{14}C$ and ${}_{11}{}^{23}N$ 

2.  ${}_{12}{}^{24}Mg$  and ${}_{11}{}^{23}C$ 

3.  ${}_2{}^{4}He$  and ${}_8{}^{16}O$ 

4.  ${}_6{}^{12}C$  and ${}_7{}^{15}N$  

Which of the following statements about the properties of X-rays is incorrect?

1.  X-rays can ionize gases.

2.  X-rays produce fluorescence in zinc sulphide (ZnS).

3.  X-rays are deflected by electric and magnetic fields.

4.  X-rays have shorter wavelengths than ultraviolet rays.

The correct expression derived for the energy of an electron in the n^th energy level is for H-atom

1.  ${\mathrm{E}}_{\mathrm{n}}=\frac{2{\mathrm{\pi }}^2<mspace\; width="1em"></mspace>{\mathrm{me}}^4<mspace\; width="1em"></mspace>{\mathrm{K}}^2}{{\mathrm{n}}^2<mspace\; width="1em"></mspace>{\mathrm{h}}^2}$

2.  ${\mathrm{E}}_{\mathrm{n}}=-\frac{{\mathrm{\pi }}^2<mspace\; width="1em"></mspace>{\mathrm{me}}^4<mspace\; width="1em"></mspace>{\mathrm{K}}^2}{2{\mathrm{n}}^2<mspace\; width="1em"></mspace>{\mathrm{h}}^2}$

3.  ${\mathrm{E}}_{\mathrm{n}}=-\frac{2{\mathrm{\pi }}^2<mspace\; width="1em"></mspace>{\mathrm{me}}^2<mspace\; width="1em"></mspace>{\mathrm{K}}^2}{{\mathrm{n}}^2<mspace\; width="1em"></mspace>{\mathrm{h}}^2}$

4.  ${\mathrm{E}}_{\mathrm{n}}=-\frac{2{\mathrm{\pi }}^2<mspace\; width="1em"></mspace>{\mathrm{me}}^4<mspace\; width="1em"></mspace>{\mathrm{K}}^2}{{\mathrm{n}}^2<mspace\; width="1em"></mspace>{\mathrm{h}}^2}$

For any H-like system, the ratio of velocities of I, II & III orbit i.e., ${\mathrm{V}}_1<mspace\; width="1em"></mspace>:<mspace\; width="1em"></mspace>{\mathrm{V}}_2<mspace\; width="1em"></mspace>:<mspace\; width="1em"></mspace>{\mathrm{V}}_3$ will be:

1.  1 : 2 : 3

2.  1 : 1/2 : 1/3

3.  3 : 2 : 1

4.  1 : 1 : 1