What is the ratio of the energies of the hydrogen atom in its first and second excited states?

1.	\(\dfrac{1}{4}\)	2.	\(\dfrac{4}{9}\)
3.	\(\dfrac{9}{4}\)	4.	\(4\)

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

(1) $2\times {10}^5 m/s$             (2) $2\times {10}^6 m/s$

(3) $2\times {10}^7 m/s$             (4) $2\times {10}^8 m/s$

 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) $\frac{\sqrt{4{\mathrm{\pi \epsilon }}_0{\mathrm{a}}_0\mathrm{m}}}{e}$

The energy of an electron in excited hydrogen atom is -3.4 eV. Then according to Bohr's theory, the angular momentum of the electron in Js is

(1) $2.11 \times {10}^{-34} Js$

(2) $3 \times {10}^{-34} Js$

(3) $2\times {10}^{-34} Js$

(4) $0.5 \times {10}^{-34} Js$

When hydrogen atom is in its first excited level, its radius is [1997]

(1) four times, its ground state radius

(2) twice, its ground state radius

(3) same as its ground state radius

(4) half of its ground state radius

The ionisation potential of helium atom is 24.6 volt, the energy required to ionise it will be

(1) 24.6 eV            (2) 24.6 volt          (3) 13.6 volt                 (4) 13..6 eV

The ionisation energy of hydrogen atom is 13.6 eV, the ionisation energy of helium atom would be [1988]

(1) 13.6 eV            (2) 27.2 eV           (3) 6.8 eV            (4) 54.4 eV

If an electron in an hydrogen atom jumps from an orbit $n_i=3$ to an orbit with level $n_f=2$, the frequency of the emitted radiation is 

(1) $v=\frac{36 C}{5 R}$               (2) v = $\frac{CR}{6}$                (3) v = $\frac{5 RC}{36}$             (4) v  = $\frac{6 C}{R}$