An alpha nucleus of energy \({1 \over 2 } mv^2\) bombards a heavy nuclear target of charge \(Ze\). Then the distance of the closest approach for the alpha nucleus will be proportional to: 
1. \(v^2\)
2. \(1/ v^4\)
3. \(1 /m\)
4. \(1/Ze\)

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. \(1:-2\)

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. \(3.0\times 10^{8}~\text{m/s}\)

According to Bohr's theory, the moment of momentum of an electron revolving in second orbit of hydrogen atom will be:
1. \(2\pi h\)
2. \(\pi h\) 
3. \(\frac{h}{\pi}\)
4. \(\frac{2h}{\pi}\)

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