If an alpha nucleus of energy $\frac{1}{2}m{v}^2$ bombards a heavy nuclear target of charge Ze, then the distance of closest approach for the alpha nucleus will be proportional to:

1.	\(\frac{1}{Ze} \)	2.	\(v^2 \)
3.	\(\frac{1}{m} \)	4.	\(\frac{1}{v^4}\)

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

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 total acceleration of the electron in a singly ionised helium atom and a hydrogen atom (both in the ground state) is:

1. 1             

2. 8

3. 4

4. 16

An electron revolves around a nucleus of charge Ze. In order to excite the electron from the state n=3 to n=4, the energy required is 66.0 eV. The value of Z will be:

1. 25 

2. 10

3. 4 

4. 5

How much is the total energy of an electron in the first orbit of a hydrogen atom equal to?

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. $\frac{4}{3}$