A hydrogen atom is in an excited state of principal quantum number \((n)\). It emits a photon of wavelength \((\lambda)\) when it returns to the ground state. The value of \(n\) is:
1. \(\sqrt{\frac{\lambda R}{\lambda R-1}}\)
2. \(\sqrt{\frac{(\lambda R-1)}{\lambda R}}\)
3. \(\sqrt{\lambda(R-1)}\)
4. None of these

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