If an electron in a hydrogen atom jumps from the \(3^{\text{rd}}\) orbit to the \(2^{\text{nd}}\) orbit, it emits a photon of wavelength \(\lambda\)$$. When it jumps from the \(4^{\text{th}}\) orbit to the \(3^{\text{rd}}\) orbit, the corresponding wavelength of the photon will be:

1.	\(\frac{16}{25}\lambda\)	2.	\(\frac{9}{16}\lambda\)
3.	\(\frac{20}{7}\lambda\)	4.	\(\frac{20}{13}\lambda\)

The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is:
1. \(1\)
2. \(4\)
3. \(0.5\)
4. \(2\)

The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom is:
1. \(1:1\)
2. \(1:-1\)
3. \(2:-1\)
4. \(1:-2\)

Given that the value of the Rydberg constant is \(10^{7}~\text{m}^{-1}\), what will be the wave number of the last line of the Balmer series in the hydrogen spectrum?
1. \(0.5 \times 10^{7}~\text{m}^{-1}\)
2. \(0.25 \times 10^{7} ~\text{m}^{-1}\)
3. \(2.5 \times 10^{7}~\text{m}^{-1}\)
4. \(0.025 \times 10^{4} ~\text{m}^{-1}\)

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

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. \(2.5\times10^{15}~\text{Hz}\)