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×${10}^{-6}$ m/s)

$$\begin{gathered} 1. 7.6\times {10}^{13} \mathrm{Hz} \\ 2. 4.7\times {10}^{15} \mathrm{Hz} \\ 3. 6.6\times {10}^{15} \mathrm{Hz} \\ 4. 5.2\times {10}^{13} \mathrm{Hz} \end{gathered}$$

A 10 kg satellite circles earth once every 2 h in an orbit having a radius of 8000 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:

$$\begin{gathered} 1. 2.0\times {10}^{43} \\ 2. 4.7\times {10}^{45} \\ 3. 3.0\times {10}^{43} \\ 4. 5.3\times {10}^{45} \end{gathered}$$

The wavelength of the first spectral line of the Lyman series of the hydrogen spectrum is:

1. 1018 Å

2. 974.3 Å

3. 2124 Å

4. 2120 Å

It is found experimentally that 13.6 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:

$$\begin{gathered} 1. 3.2\times {10}^6 \mathrm{m}/\mathrm{s} \\ 2. 2.2\times {10}^6 \mathrm{m}/\mathrm{s} \\ 3. 4.2\times {10}^6 \mathrm{m}/\mathrm{s} \\ 4. 1.2\times {10}^6 \mathrm{m}/\mathrm{s} \end{gathered}$$

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

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.)

1. the earth will be closer to the sun than it is actually.

2. the earth will be farther away from the sun than it is actually.

3. the earth remains at the same distance from the sun as it is actually.

4. None of these