If the series limit frequency of the Lyman series is \(\nu_L\), then the series limit frequency of the Pfund series is:
1. \(25\nu_L\)
2. \(16\nu_L\)
3. \(\nu_L/16\)
4. \(\nu_L/25\)

An X-ray tube is operated at \(1.24\) million volt. The shortest wavelength of the produced photon will be :
1. \(10^{-3}\) nm
2. \(10^{-1}\) nm
3. \(10^{-2}\) nm
4. \(10^{-4}\) nm

According to Bohr atom model, in which of the following transitions will the frequency be maximum ?
1. \(n=4 \) to \(n=3\)
2. \(n=2\) to \(n=1\)
3. \(n=5\) to \(n=4 \)
4. \(n=3\) to \(n=2\)

Some energy levels of a molecule are shown in the figure. The ratio of the wavelength \(r=\frac{\lambda_1}{\lambda_2}\), is given by:

                
1. \( r=\frac{4}{3} \)
2. \( r=\frac{2}{3} \)
3. \( r=\frac{3}{4} \)
4. \( r=\frac{1}{3}\)

The recoil speed of a hydrogen atom after it emits a photon in going from \(n=5\) state to \(n =1\) state will be:
1. \(4.17\) m/s
2. \(2.19\) m/s
3. \(3.25\) m/s
4. \(4.34\) m/s

Hydrogen \(({ }_1 \mathrm{H}^1)\), Deuterium \(({ }_1 \mathrm{H}^2)\), singly ionised Helium \(({ }_2 \mathrm{He}^4)^+\) and doubly ionised lithium \(({ }_3 \mathrm{Li}^6)^{++}\) all have one electron around the nucleus. Consider and electron transition from \(n=2\) to \(n=1\). If the wavelengths of emitted radiation are \(\lambda_1,\lambda_2,\lambda_3\) and \(\lambda_4\) respectively then approximately which one of the following is correct?
1. \( \lambda_1=2 \lambda_2=2 \lambda_3=\lambda_4 \)
2. \( \lambda_1=\lambda_2=4 \lambda_3=9 \lambda_4 \)
3. \( \lambda_1=2 \lambda_2=3 \lambda_3=4 \lambda_4 \)
4. \( 4 \lambda_1=2 \lambda_2=2 \lambda_3=\lambda_4\)

As an electron makes a transition from an excited state to the ground state of a hydrogen-like atom/ion:

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let \(\lambda_n,\lambda_g\) be the de Broglie wavelength of the electron in the \(n^{\text{th}}\) state and the ground state respectively. Let \(\Lambda_n\) be the wavelength of the emitted photon in the transition from the \(n^{\text{th}}\) state to the ground state. For large \(n\), (\(A,B\) are constants)
1. \( \Lambda_{{n}} \approx {A}+\frac{{B}}{\lambda_{{n}}^2} \)
2. \( \Lambda_{{n}} \approx {A}+{B} \lambda_{{n}} \)
3. \( \Lambda_{{n}}{ }^2 \approx {A}+{B} \lambda_{{n}}{ }^2 \)
4. \(\Lambda_{{n}}{ }^2 \approx \lambda \)

If \(\lambda_1\)​ represents the wavelength of the third member of the Lyman series and \(\lambda_2\)​ represents the wavelength of the first member of the Paschen series, then the ratio \(\lambda_1:\lambda_2\)​ is:
1. \(1:9\)
2. \(7:108\)
3. \(7:135\)
4. \(1:3\)

The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from \(n=2\) to \(n=1\) state is:
1. \(194.8~\text{nm}\) 
2. \(913.3~\text{nm}\) 
3. \(490.7~\text{nm}\) 
4. \(121.8~\text{nm}\)