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 the closest approach is \(r_0\). The energy of the projectile is:

1.	directly proportional to \(M_1M_2\).
2.	directly proportional to \(Z_1Z_2\).
3.	inversely proportional to \(Z_1\).
4.	directly proportional to mass \(M_1\).

Consider \(3^{\text{rd}}\) orbit of \(He^{+}\) (Helium). Using a non-relativistic approach, the speed of the electron in this orbit will be: (given \(Z=2\) and \(h\) (Planck's constant)\(= 6.6\times10^{-34}~\text{J-s}\))
1. \(2.92\times 10^{6}~\text{m/s}\)
2. \(1.46\times 10^{6}~\text{m/s}\)
3. \(0.73\times 10^{6}~\text{m/s}\)
4. \(3.0\times 10^{8}~\text{m/s}\)

The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom is:
1. \(1:1\)
2. \(1:-1\)
3. \(2:-1\)
4. \(1:-2\)

The transition from the state n = 3 to n = 1 in a hydrogen-like atom results in ultraviolet radiation. How will the Infrared radiation be obtained in the transition?

1. 4 $\to$ 2 

2. 4 $\to$3

3. 2 $\to$ 1 

4. 3 $\to$ 2

Which statement about the Rutherford model of the atom is not true?

Ratio of the wavelengths of first line of Lyman series and first line of Balmer series is:

1. 1: 3                 

2. 27 : 5

3. 5 : 27               

4. 4 : 9

The de-Broglie wavelength of an electron in the first Bohr orbit is:
1. Equal to one-fourth the circumference of the first orbit
2. Equal to half the circumference of the first orbit
3. Equal to twice the circumference of the first orbit
4. Equal to the circumference of the first orbit

If the energy of the electron in an \(\mathrm{H}\)-atom in the ground state is taken to be \(-13.6\) eV, then the kinetic energy of the electron in the first excited state will be:
1. \(3.4\) eV
2. \(6.8\) eV
3. \(10.2\) eV
4. \(13.6\) eV