Consider \(3^{\text{rd}}\) orbit of \(He^{+}\) (Helium). Using a non-relativistic approach, the speed of the electron in this orbit will be: (given \(Z=2\) and \(h\) (Planck's constant)\(= 6.6\times10^{-34}~\text{J-s}\))
1. \(2.92\times 10^{6}~\text{m/s}\)
2. \(1.46\times 10^{6}~\text{m/s}\)
3. \(0.73\times 10^{6}~\text{m/s}\)
4. \(3.0\times 10^{8}~\text{m/s}\)

The hydrogen gas with its atoms in the ground state is excited by monochromatic radiation of \(\lambda = 975~\mathring{\text{A}}\). The number of spectral lines in the resulting spectrum emitted will be:
1. \(3\)
2. \(2\)
3. \(6\)
4. \(10\)

The ratio of the longest wavelengths corresponding to the Lyman and Balmer series in the hydrogen spectrum is:

Electron in hydrogen atom first jumps from the third excited state to the second excited state and then from the second excited to the first excited state. The ratio of the wavelengths \(\lambda_1:\lambda_2\) emitted in the two cases is:
1. \(\frac{7}{5}\)
2. \(\frac{20}{7}\)
3. \(\frac{27}{5}\)
4. \(\frac{27}{20}\)

An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be:
(\(m\) is the mass of hydrogen atom, \(R\) is Rydberg constant and \(h\) is Plank’s constant)
1. \(\frac{24m}{25hR}\)
2. \(\frac{25hR}{24m}\)
3. \(\frac{25m}{24hR}\)
4. \(\frac{24hR}{25m}\)

Monochromatic radiation emitted when electron on hydrogen atom jumps from first excited to the ground state irradiates a photosensitive material. The stopping potential is measured to be \(3.57~\text{V}\). The threshold frequency of the material is:
1. \(4\times10^{15}~\text{Hz}\)
2. \(5\times10^{15}~\text{Hz}\)
3. \(1.6\times10^{15}~\text{Hz}\)
4. \(2.5\times10^{15}~\text{Hz}\)

The energy of a hydrogen atom in the ground state is \(-13.6\) eV. The energy of a He⁺ ion in the first excited state will be:
1. \(-13.6\) eV
2. \(-27.2\) eV
3. \(-54.4\) eV
4. \(-6.8\) eV

If an alpha nucleus of energy $\frac{1}{2}m{v}^2$ bombards a heavy nuclear target of charge Ze, then the distance of closest approach for the alpha nucleus will be proportional to: