When an \(\alpha\text-\)particle of mass \(m\) moving with velocity \(v\) bombards on a heavy nucleus of charge \(Ze\), its distance of closest approach from the nucleus depends on \(m\) as:

1.	\(\dfrac{1}{\sqrt{m}}\)	2.	\(\dfrac{1}{m^{2}}\)
3.	\(m\)	4.	\(\dfrac{1}{m}\)

In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is:

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 \(\lambda = 975~\mathring{{A}}.\) The number of spectral lines in the resulting spectrum emitted will be:
1. \(3\)
2. \(2\)
3. \(6\)
4. \(10\)

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