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. \(10\)

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. \(\dfrac{24m}{25hR}\)
2. \(\dfrac{25hR}{24m}\)
3. \(\dfrac{25m}{24hR}\)
4. \(\dfrac{24hR}{25m}\)

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 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. \(2\rightarrow 1\)