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

Select the incorrect graph for velocity of ${\mathrm{e}}^{-}$ in an orbit $\mathrm{vs}.<mspace\; width="1em"></mspace>\mathrm{Z},<mspace\; width="1em"></mspace>\frac{1}{\mathrm{n}}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\mathrm{n}$:

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 \(E~ vs . Z^ 2\) (keeping "n" constant) will be:

1.		2.
3.		4.