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

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. \(5.3\times10^{45}\)$\mathrm{}$

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)

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. \(1.2\times10^6~\text{m/s}\)$\mathrm{}$

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 \(10^{-15}~\text{m}\)) 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 \(1.5\times 10^{11}~\text{m}\). The radius of the sun is taken as \(7\times10^{8}~\text{m}\).)

The total energy of an electron in the \(n^{th}\) stationary orbit of the hydrogen atom can be obtained by:
1. \(E_n = \frac{13.6}{n^2}~\text{eV}\)
2. \(E_n = -\frac{13.6}{n^2}~\text{eV}\)
3. \(E_n = \frac{1.36}{n^2}~\text{eV}\)
4. \(E_n = -{13.6}\times{n^2}~\text{eV}\)

The simple Bohr model is not applicable to He⁴ atom because

(a) He⁴ is an inert gas
(b) He⁴ has neutrons in the nucleus
(c) He⁴ has one more electron
(d) electrons are not subject to central forces

1. (a, c)

2. (a, c, d)

3. (b, d)

4. (c, d)

Let $E_n=\frac{-1}{8{\mathrm{\epsilon }}_0^2}\frac{m{e}^4}{n^2{h}^2}$ be the energy of the nth level of H-atom. If all the H-atoms are in the ground state and radiation of frequency $\frac{(E_2-E_1)}{h}$ falls on it,

(a) it will not be absorbed at all
(b) some of the atoms will move to the first excited state
(c) all atoms will be excited to the n = 2 state
(d) no atoms will make a transition to the n = 3 state

1. (b, d)

2. (a, d)

3. (b, c, d)

4. (c, d)

The Balmer series for the H-atom can be observed:
 

1. (b, c)

2. (a, c)

3. (b, d)

4. (c, d)