Consider an electron in the \(n^\mathrm{th}\) 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. \((13.6)n\lambda\)
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 ground state energy of H-atom is 13.6 eV. The energy needed to ionise H-atom from its second excited state [1991]

1. 1.51 eV

2. 3.4 eV

3. 13.6 eV

4. 12.1 eV

          
1. \(\frac{\lambda}{3}\)
2. \(\frac{3\lambda}{4}\)
3. \(\frac{4\lambda}{3}\)
4. \(3\lambda\)

The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 $\stackrel{0}{A}$. The wavelength of the second spectral line in the Balmer series of singly ionized helium atom is [IIT-JEE 2011]

1. 1215 $\stackrel{0}{A}$ 

2. 1640 $\stackrel{0}{A}$

3. 2430 $\stackrel{0}{A}$ 

4. 4687 $\stackrel{0}{A}$

Energy 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 [2004]

1. 1.5 eV 

2. 0.85 eV 

3. 3.4 eV 

4. 1.9 eV

The energy of ground electronic state of hydrogen atom is -13.6 eV.  The energy of the first excited state will be [1997]

1. -54.4 eV 

2. -27.2 eV

3. -6.8 eV 

4. -3.4 eV

The total energy of an electron in the first excited state of hydrogen is about -3.4 eV. Its kinetic energy in this state is [2005]

1. -3.4 eV

2. -6.8 eV 

3. 6.8 eV 

4. 3.4 eV

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