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.  

Number of waves produced by an electron in one complete revolution in n^th orbit is:

1.  $\mathrm{n}$

2.  ${\mathrm{n}}^2$

3.  $\left(\mathrm{n}+1\right)$

4.  $\left(2\mathrm{n}+1\right)$

The energy of an electron moving in n^th Bohr's orbit of an element is given by ${\mathrm{E}}_{\mathrm{n}}=\frac{-13.6}{{\mathrm{n}}^2}{\mathrm{Z}}^2$ eV/atom (Z=atomic number). The graph of $\mathrm{E} \mathrm{vs}. {\mathrm{Z}}^2$ (keeping "n" constant) will be:

1.		2.
3.		4.

The spectrum produced from an element is:

1.  atomic spectrum

2.  line spectrum

3.  absorption spectrum

4.  any one of the above

Which of the following expressions represents the spectrum of Balmer series (If n is the principal quantum number of higher energy level) in Hydrogen atom?

1.  $\overline{\mathrm{v}}=\frac{\mathrm{R}\left(\mathrm{n}-1\right) \left(\mathrm{n}+1\right)}{{\mathrm{n}}^2} {\mathrm{cm}}^{-1}$

2.  $\overline{\mathrm{v}}=\frac{\mathrm{R}\left(\mathrm{n}-2\right) \left(\mathrm{n}+2\right)}{4{\mathrm{n}}^2} {\mathrm{cm}}^{-1}$

3.  $\overline{\mathrm{v}}=\frac{\mathrm{R}\left(\mathrm{n}-2\right) \left(\mathrm{n}+2\right)}{{\mathrm{n}}^2} {\mathrm{cm}}^{-1}$

4.  $\overline{\mathrm{v}}=\frac{\mathrm{R}\left(\mathrm{n}-1\right) \left(\mathrm{n}+1\right)}{4{\mathrm{n}}^2} {\mathrm{cm}}^{-1}$