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. \(E_n = -{13.6}\times{n^2}~\text{eV}\)

The transition from the state \(n=3\) to \(n=1\) in hydrogen-like atoms results in ultraviolet radiation. Infrared radiation will be obtained in the transition from:
1. \(3\rightarrow 2\)
2. \(4\rightarrow 2\)
3. \(4\rightarrow 3\)
4. \(2\rightarrow 1\)

An electron in the hydrogen atom jumps from the excited state n to the ground state. The wavelength so emitted illuminates a photosensitive material having a work function of 2.75 eV. If the stopping potential of the photoelectron is 10V, then the value of n is:
1. 2
2. 3
3. 4
4. 5

Out of the following which one is not possible energy for a photon to be emitted by hydrogen atom according to Bohr's atomic model?

1. 0.65 eV

2. 1.9 eV

3. 11.1 eV

4. 13.6 eV

The electrons in the hydrogen atom jump from the excited state (n = 3) to its ground state (n = 1) and the photons thus emitted irradiate a photosensitive material. If the work function of the material is 5.1 eV, the stopping potential is estimated to be (the energy of the electron in nth state $E_n=-\frac{13.6}{n^2}eV$):
1. 12.1 V

2. 17.2 V

3. 7 V

4. 5.1 V

Maximum frequency of emission is obtained for the transition:

1. n = 2 to n = 1

2. n = 6 to n = 2

3. n = 1 to n = 2

4. n = 2 to n = 6

The total energy of an electron in the first excited state of a hydrogen atom is about –3.4 eV. Its kinetic energy in this state will be:

1. –6.8 eV

2. 3.4 eV

3. 6.8 eV

4. –3.4 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. \(\lambda_3=\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2}\)

In the Bohr model of H-atom, an electron (e) is revolving around a proton (p) with velocity v. If r is the radius of the orbit, m is the mass and ${\epsilon }_0$ is vacuum permittivity, then the value of v is:

1.  $\frac{e}{\sqrt{4{\mathrm{\pi m\epsilon }}_0\mathrm{r}}}$

2. $\frac{2e}{\sqrt{{\mathrm{\pi m\epsilon }}_0\mathrm{r}}}$

3. $\frac{e}{\sqrt{{\mathrm{\pi m\epsilon }}_0\mathrm{r}}}$

4. $\frac{e}{4{\mathrm{\pi m\epsilon }}_{0}r}$

The life span of atomic hydrogen is:

1. Fraction of one sec

2. One year

3. One hour

4. One day