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.  $\frac{{\mathrm{a}}_0}{\sqrt{2}}$

The Schrodinger wave equation for hydrogen atom is $\mathrm{\psi }\left(\mathrm{radial}\right)=\frac{1}{16\sqrt{4}}{\left(\frac{\mathrm{Z}}{{\mathrm{a}}_0}\right)}^{3/2} \left[\left(\mathrm{\sigma }-1\right) \left({\mathrm{\sigma }}^2-8\mathrm{\sigma }+12\right)\right]{\mathrm{e}}^{-\mathrm{\sigma }/2}$ 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.  $\frac{{\mathrm{a}}_0}{\mathrm{Z}}, \frac{3{\mathrm{a}}_0}{\mathrm{Z}}$

2. $\frac{{\mathrm{a}}_0}{2\mathrm{Z}}, \frac{{\mathrm{a}}_0}{\mathrm{Z}}$

3.  $\frac{{\mathrm{a}}_0}{2\mathrm{Z}}, \frac{3{\mathrm{a}}_0}{\mathrm{Z}}$

4.  $\frac{{\mathrm{a}}_0}{2\mathrm{Z}}, \frac{4{\mathrm{a}}_0}{\mathrm{Z}}$

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 ${}_7{}^{15}N$  

The incorrect statement regarding the characteristics of X-rays is :

1. The radiation can ionize the gas

2. It causes a fluorescence effect on ZnS

3. It is deflected by electric and magnetic fields

4. Have a shorter wavelength than ultraviolet rays

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

1.  ${\mathrm{E}}_{\mathrm{n}}=\frac{2{\mathrm{\pi }}^2 {\mathrm{me}}^4 {\mathrm{K}}^2}{{\mathrm{n}}^2 {\mathrm{h}}^2}$

2.  ${\mathrm{E}}_{\mathrm{n}}=-\frac{{\mathrm{\pi }}^2 {\mathrm{me}}^4 {\mathrm{K}}^2}{2{\mathrm{n}}^2 {\mathrm{h}}^2}$

3.  ${\mathrm{E}}_{\mathrm{n}}=-\frac{2{\mathrm{\pi }}^2 {\mathrm{me}}^2 {\mathrm{K}}^2}{{\mathrm{n}}^2 {\mathrm{h}}^2}$

4.  ${\mathrm{E}}_{\mathrm{n}}=-\frac{2{\mathrm{\pi }}^2 {\mathrm{me}}^4 {\mathrm{K}}^2}{{\mathrm{n}}^2 {\mathrm{h}}^2}$

For any H-like system, the ratio of velocities of I, II & III orbit i.e., ${\mathrm{V}}_1 : {\mathrm{V}}_2 : {\mathrm{V}}_3$ will be:

1.  1 : 2 : 3

2.  1 : 1/2 : 1/3

3.  3 : 2 : 1

4.  1 : 1 : 1

Select the incorrect graph for velocity of ${\mathrm{e}}^{-}$ in an orbit $\mathrm{vs}. \mathrm{Z}, \frac{1}{\mathrm{n}} \mathrm{and} \mathrm{n}$:

1.  

2.  

3.  

4.