Taking the bohr radius as \(a_0=53\) pm, the radius of Li⁺⁺ ion in its ground state on the basis of bohr's model will be about:
1. \(153\) pm
2. \(27\) pm
3. \(18\) pm
4. \(13\) pm

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

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 \(7.7\text{ MeV}\) \(\alpha\)-particle before it comes momentarily to rest and reverses its direction?
1. \(10\text{ fm}\)
2. \(25\text{ fm}\)
3. \(30\text{ fm}\)
4. \(35\text{ fm}\)

The minimum orbital angular momentum of the electron in a hydrogen atom is:
1. \(h\)
2. \(h/2\)
3. \(h/2\pi\)
4. \(h/ \lambda\)

Which of the following transitions will the wavelength be minimum?
1. \(n=5~\text{to}~n=4\)
2. \(n=4~\text{to}~n=3\)
3. \(n=3~\text{to}~n=2\)
4. \(n=2~\text{to}~n=1\)

In which of the following systems will the wavelength corresponding to \(n=2\) to \(n=1\) be minimum?

The transition from the state \(n=3\) to \(n=1\) in hydrogen-like atoms results in ultraviolet radiation. Infrared radiation will be obtained in the transition from:
1. \(3\rightarrow 2\)
2. \(4\rightarrow 2\)
3. \(4\rightarrow 3\)
4. \(2\rightarrow 1\)