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

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 life span of atomic hydrogen is:

1. Fraction of one sec

2. One year

3. One hour

4. One day

When an electron transitions from n = 4 to n = 2, then the emitted line in the spectrum will be:

If the energy of the hydrogen atom in $n^{th}$ orbit is $E_n$, then the energy in $n^{th}$ orbit of the singly ionised helium atom will be:
1.  4$E_n$
2.  $E_n$/4
3.  2$E_n$
4.  $E_n$/2

An electron is moving around the nucleus of a hydrogen atom in a circular orbit of radius r. What is the coulomb force $\overrightarrow{\mathrm{F}}$ between the two? \(\left ( \text{where},K=\frac{1}{4\pi \epsilon _{0}} \right )\)

1. $\mathrm{K}\frac{{\mathrm{e}}^2}{{\mathrm{r}}^2}\hat{\mathrm{r}}$

2. $-\mathrm{K}\frac{{\mathrm{e}}^2}{{\mathrm{r}}^3}\hat{\mathrm{r}}$

3. $\mathrm{K}\frac{{\mathrm{e}}^2}{{\mathrm{r}}^3}\overrightarrow{\mathrm{r}}$

4. $-\mathrm{K}\frac{{\mathrm{e}}^2}{{\mathrm{r}}^3}\overrightarrow{\mathrm{r}}$

In which of the following systems will the radius of the first orbit (n = 1) be minimum:

1. doubly ionized lithium

2. singly ionized helium

3. deuterium atom

4. hydrogen atom

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

The Bohr model of atoms:
 

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