Electrons of mass m with de- Broglie wavelength λ fall on the target in an X-ray tube. The cut-off wavelength (λo) of the emitted X-ray is:
1.
2.
3.
4.
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:
1. | \(\frac{4}{9}\) | 2. | \(\frac{9}{4}\) |
3. | \(\frac{27}{5}\) | 4. | \(\frac{5}{27}\) |
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:
1. | \(\frac{3}{23}\) | 2. | \(\frac{7}{29}\) |
3. | \(\frac{9}{31}\) | 4. | \(\frac{5}{27}\) |
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. \(\frac{24hR}{25m}\)