The total energy of an electron in the \(n^{th}\) stationary orbit of the hydrogen atom can be obtained by:
1. \(E_n = \frac{13.6}{n^2}~\text{eV}\)
2. \(E_n = -\frac{13.6}{n^2}~\text{eV}\)
3. \(E_n = \frac{1.36}{n^2}~\text{eV}\)
4. \(E_n = -{13.6}\times{n^2}~\text{eV}\)

Energy levels A, B and C of a certain atom correspond to increasing values of energy i.e. \(E_A<E_B<E_C\).  If \(\lambda_1, ~\lambda_2\) and \(\lambda_3\) are wavelengths of radiations corresponding to transitions C to B, B to A and C to A respectively, which of the following relations is correct?
1. \(\lambda_3=\lambda_1+\lambda_2\)
2. \(\lambda_1+\lambda_2+\lambda_3=0\)
3. \(\lambda_3^2=\lambda_1^2+\lambda_2^2\)
4. \(\lambda_3=\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2}\)

The life span of atomic hydrogen is:

1. Fraction of one sec

2. One year

3. One hour

4. One day

Energy \(E\) of a hydrogen atom with principal quantum number \(n\) is given by \(E=-\frac{13.6}{n^{2}}~\text{eV}.\) The energy of a photon ejected when the electron jumps from \(n=3\) state to \(n=2\) state of hydrogen is approximately:
1. \(0.85~\text{eV}\)
2. \(3.4~\text{eV}\)
3. \(1.9~\text{eV}\)
4. \(1.5~\text{eV}\)

Taking the wavelength of first Balmer line in hydrogen spectrum \((n=3~\text{to}~n=2)\) as \(660~\text{nm}\), the wavelength of the \(2^{nd}\) Balmer line \((n=4~\text{to}~n=2)\) will be:
1. \(889.2~\text{nm}\)
2. \(388.9~\text{nm}\)
3. \(488.9~\text{nm}\)
4. \(642.7~\text{nm}\)

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, \(\lambda_1/\lambda_2\) of the photons emitted in this process is:
1. \(22/5\)
2. \(7/5\)
3. \(9/7\)
4. \(20/7\)

A \(\mathrm{He}^+\) ion is in its first excited state. Its ionization energy is:
1. \(48.36~\text{eV}\)
2. \(13.60~\text{eV}\)
3. \(54.40~\text{eV}\)
4. \(6.04~\text{eV}\)

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. \(121.8~\text{nm}\) 

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 \(n=2\)