The ionisation energy of a hydrogen atom is \(13.6~\text{eV}\). Following Bohr's theory, what is the energy corresponding to a transition between the \(3^{th}\) and \(4^{th}\) orbit?
1. \(3.40~\text{eV}\)
2. \(1.51~\text{eV}\)
3. \(0.85~\text{eV}\)
4. \(0.66~\text{eV}\)

The ratio of the energies of the hydrogen atom in its first to second excited states is

1. $\frac{1}{4}$ 

2. $\frac{4}{9}$

3. $\frac{9}{4}$

4. 4

Energy levels A, B, C of a certain atom correspond to increasing values of energy i.e. $E_A<E_B<E_C.$ If ${\lambda }_1,<mspace\; width="1em"></mspace>{\lambda }_2,<mspace\; width="1em"></mspace>{\lambda }_3$ are the wavelengths of the radiation corresponding to the transitions C to B, B to A and C to A respectively, which of the following relation is correct?

1. ${\lambda }_3={\lambda }_1+{\lambda }_2$ 

2. ${\lambda }_3=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$

3. ${\lambda }_1+{\lambda }_2+{\lambda }_3=0$ 

4. ${\lambda }_3^2={\lambda }_1^2+{\lambda }_2^2$

In the Rutherford scattering experiment, what will be the correct angle for $\propto$-scattering for an impact parameter, b = 0?

1. ${90}^{\circ }$

2. ${270}^{\circ }$

3. $0^{\circ }$ 

4. ${180}^{\circ }$

The velocity of the electron in the ground state (H - atom) is 

1. $2.18\times {10}^5<mspace\; width="1em"></mspace>m/s$   

2. $2.18\times {10}^6<mspace\; width="1em"></mspace>m/s$

3. $2.18\times {10}^7<mspace\; width="1em"></mspace>m/s$   

4. $2.18\times {10}^8<mspace\; width="1em"></mspace>m/s$

The element which has K$\alpha$ X-ray line whose wavelength is 0.18 nm is:

1. Cobalt 

2.  Xenon

3. Copper 

4. Iron

Calculate the highest frequency of the emitted photon in the Paschen series of spectral lines of the Hydrogen atom:

1. $3.7\times {10}^{14}<mspace\; width="1em"></mspace>Hz$ 

2. $9.1\times {10}^{15}<mspace\; width="1em"></mspace>Hz$

3. $10.23\times {10}^{14}<mspace\; width="1em"></mspace>Hz$

4. $29.7\times {10}^{15}<mspace\; width="1em"></mspace>Hz$

Which of the following transitions gives photon of maximum energy?

1. n = 1 to n = 2 

2. n = 2 to n = 1

3. n = 2 to n = 6 

4. n = 6 to n = 2

Hydrogen atoms are excited from ground state of the principal quantum number 4. Then, the number of spectral lines observed will be

1. 3   

2. 6

3. 5

4. 2