In Rutherford’s nuclear model of the atom, the nucleus (radius about 10^-15 m) is analogous to the sun about which the electron move in orbit (radius ≈ 10^-10 m) like the earth orbits around the sun. If the dimensions of the solar system had the same proportions as those of the atom, then:

(The radius of the earth's orbit is about 1.5 x 10¹¹m. The radius of the sun is taken as 7 x 10⁸m.)

In a Geiger-Marsden experiment, what is the distance of the closest approach to the nucleus of a \(7.7\) MeV \(\alpha\)-particle before it comes momentarily to rest and reverses its direction?
1. \(10\) fm
2. \(25\) fm
3. \(30\) fm
4. \(35\) fm

It is found experimentally that \(13.6~\text{eV}\) energy is required to separate a hydrogen atom into a proton and an electron. The velocity of the electron in a hydrogen atom is:
1. \(3.2\times10^6~\text{m/s}\)
2. \(2.2\times10^6~\text{m/s}\)
3. \(3.2\times10^6~\text{m/s}\)
4. \(1.2\times10^6~\text{m/s}\)$\mathrm{}$

According to the classical electromagnetic theory, the initial frequency of the light emitted by the electron revolving around a proton in the hydrogen atom is: (The velocity of the electron moving around a proton in a hydrogen atom is \(2.2\times10^{6}\) m/s)
1. \(7.6\times10^{13}\) Hz
2. \(4.7\times10^{15}\) Hz
3. \(6.6\times10^{15}\) Hz
4. \(5.2\times10^{13}\) Hz$\mathrm{}$

A \(10~\text{kg}\) satellite circles earth once every \(2~\text{h}\) in an orbit having a radius of \(8000~\text{km}\). Assuming that Bohr’s angular momentum postulate applies to satellites just as it does to an electron in the hydrogen atom. The quantum number of the orbit of the satellite is:
1. \(2.0\times10^{43}\)
2. \(4.7\times10^{45}\)
3. \(3.0\times10^{43}\)
4. \(5.3\times10^{45}\)$\mathrm{}$

The wavelength of the first spectral line of the Lyman series of the hydrogen spectrum is:
1. \(1218\) Å
2. \(974.3\) Å
3. \(2124\) Å
4. \(2120\) Å