In Rutherford’s nuclear model of the atom, the nucleus (radius about $10^{-15}~\text{m}$) is analogous to the sun about which the electron move in orbit (radius $\approx 10^{-10}~\text{m}$) 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 $1.5\times 10^{11}~\text{m}$ and the radius of the sun is taken as $7\times10^{8}~\text{m}$.)

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. $1.2\times10^6~\text{m/s}$

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)

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. $5.3\times10^{45}$

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