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

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. $\frac{4}{3}$

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. $\frac{4}{3}$

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) 

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

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 

In a Rutherford scattering experiment when a projectile of charge $Z_1$ and mass $M_1$ approaches a target nucleus of charge $Z_2$ and mass $M_2,$ the distance of closest approach is $r_0$. What is the energy of the projectile?

The energy of a hydrogen atom in the ground state is \(-13.6~\mathrm{eV}\). What is the energy of a He⁺ ion in the first excited state?

1. -13.6 eV

2. -27.2 eV

3. -54.4 eV

4. -6.8 eV