The electric potential between a proton and an electron is given by $\mathrm{V}={\mathrm{V}}_0\ln \frac{\mathrm{r}}{{\mathrm{r}}_0}$ where ${\mathrm{r}}_0$ is a constant. Assuming Bohr’s model to be applicable, the variation of ${\mathrm{r}}_{\mathrm{n}}$ with n, n being the principal quantum number, is:

1. ${\mathrm{r}}_{\mathrm{n}}\propto \mathrm{n}$           

2. ${\mathrm{r}}_{\mathrm{n}}\propto 1/\mathrm{n}$

3. ${\mathrm{r}}_{\mathrm{n}}\propto {\mathrm{n}}^2$           

4. ${\mathrm{r}}_{\mathrm{n}}\propto 1/{\mathrm{n}}^2$

In a hypothetical Bohr hydrogen, the mass of the electron is doubled. What will be the energy E₀ and the radius r₀ of the first orbit?
(${\mathrm{a}}_0$ is the Bohr radius) 

What is the ratio of the longest to shortest wavelengths in Brackett series of hydrogen spectra?
1. $\frac{25}{9}$           

2. $\frac{17}{6}$

3. $\frac{9}{5}$             

4. $\frac{4}{3}$

What is the ratio of the largest to shortest wavelengths in the Lyman series of hydrogen spectra?

1. $\frac{25}{9}$        

2. $\frac{17}{6}$
3. $\frac{9}{5}$           

4. $\frac{4}{3}$

In Bohr's model if the atomic radius of the first orbit is r₀, then what will be the radius of the third orbit?
1. $\frac{{\mathrm{r}}_0}{9}$              

2. ${\mathrm{r}}_0$
3. $9{\mathrm{r}}_0$               

4. $3{\mathrm{r}}_0$

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

A beam of fast-moving alpha particles were directed towards a thin film of gold. The parts A', B', and C' of the transmitted and reflected beams corresponding to the incident parts A, B and C of the beam, are shown in the adjoining diagram. The number of alpha particles in:

In the n^th orbit, the energy of an electron is \(\mathrm{E}_{\mathrm{n}}=-\frac{13.6}{\mathrm{n}^2} \mathrm{~eV}\) for the hydrogen atom. What will be the energy required to take the electron from the first orbit to the second orbit?

1. 10.2 eV

2. 12.1 eV 

3. 13.6 eV

4. 3.4 eV 

Given that the value of the Rydberg constant is \(10^{7}~\text{m}^{-1}\), what will be the wave number of the last line of the Balmer series in the hydrogen spectrum?
1. \(0.5 \times 10^{7}~\text{m}^{-1}\)
2. \(0.25 \times 10^{7} ~\text{m}^{-1}\)
3. \(2.5 \times 10^{7}~\text{m}^{-1}\)
4. \(0.025 \times 10^{4} ~\text{m}^{-1}\)

The ratio of the longest wavelengths corresponding to the Lyman and Balmer series in the hydrogen spectrum is: