Orbital acceleration of electron is 

(1) $\frac{n^2{h}^2}{4{\mathrm{\pi }}^2{\mathrm{m}}^2{\mathrm{r}}^3}$                  (2) $\frac{n^2{h}^2}{4n^2{\mathrm{r}}^3}$

(3) $\frac{4n^2{h}^2}{{\mathrm{\pi }}^2{\mathrm{m}}^2{\mathrm{r}}^3}$                     (4) $\frac{4n^2{h}^2}{4{\mathrm{\pi }}^2{\mathrm{m}}^2{\mathrm{r}}^3}$

Consider the spectral line resulting from transition n = 2 to n = 1 in the atoms and ions given below.  The shorterst wavelength is given by

(1) Hydrogen atom

(2) Deuterium

(3) Singly ionised helium

(4) Doubly ionised lithium

If the first excitation potential of the hydrogen-like atom is V electron volt, then the ionization energy of this atom  will be:

1. V electron volt

2. $\frac{2\mathrm{V}}{4}\mathit{\hspace{0.17em}}$electron volt
3. $\frac{4\mathrm{V}}{3}$ electron volt

4. cannot be calculated by the given information

When a hydrogen atom is raised from the ground state to an excited state 

1. PE decreases and KE increases 

2. PE increases and KE decreases 

3. both KE PE decrease 

4. absorption spectrum

The ionisation energy of hydrogen atom is 13.6 eV. Following Bohr's theory, the energy corresponging to a transition between 3rd and 4th orbit is   [1992]

(1) 3.40 eV        (2) 1.51 eV        (3) 0.85        (4) 0.66 eV

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

(1) $2\times {10}^5<mspace\; width="1em"></mspace>m/s$             (2) $2\times {10}^6<mspace\; width="1em"></mspace>m/s$

(3) $2\times {10}^7<mspace\; width="1em"></mspace>m/s$             (4) $2\times {10}^8<mspace\; width="1em"></mspace>m/s$

 Consider an electron in the nth orbit of a hydrogen atom in the Bohr model. The circumference of the orbit can be expressed in terms of the de-Broglie wavelength $\lambda$ of that electron as:

(1) (0.529) n$\lambda$           (2) $\sqrt{n\lambda }$             (3) (13.6) $\lambda$         (4) n$\lambda$

In the Bohr's model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electron.  If ${\alpha }_0$ is the radius of the ground state orbit, m is the mass and e is the charge on the electron, ${\epsilon }_0$ is the vaccum permittivity, the speed of the electron is  [1998]

(1) zero          (2) $\frac{e}{\sqrt{{\epsilon }_0{a}_{0}m}}$           (3) $\frac{e}{\sqrt{4{\mathrm{\pi \epsilon }}_0{\mathrm{a}}_0\mathrm{m}}}$               (4) $\frac{\sqrt{4{\mathrm{\pi \epsilon }}_0{\mathrm{a}}_0\mathrm{m}}}{e}$