Spectrum of hydrogen atom and Bohr model basics - Question Bank

1. The angular momentum of an electron in an orbit is quantized according to the Bohr model. This quantization is expressed as:
A) mvr = n/h
B) mvr = nh
C) mvr = nh/2π
D) mvr = h/2πn
2. If an electron absorbs energy and moves from n=1 to n=3, what is the energy of the absorbed photon?
A) 13.6 eV
B) 10.2 eV
C) 12.09 eV
D) 13.05 eV
3. The Bohr model provides a good approximation for the energy levels of:
A) Methane molecule
B) Hydrogen-like species (e.g., He⁺, Li²⁺)
C) Complex organic molecules
D) Metals in solid state
4. Which spectral series of hydrogen lies in the far-infrared region?
A) Lyman
B) Balmer
C) Paschen
D) Humphreys
5. What is the value of the Rydberg constant (R_H) in cm⁻¹?
A) 109737 cm⁻¹
B) 10973 cm⁻¹
C) 1097.3 cm⁻¹
D) 109.73 cm⁻¹
6. The term 'spectrum' in the context of the hydrogen atom refers to:
A) The arrangement of protons and neutrons in the nucleus.
B) The pattern of wavelengths of light emitted or absorbed by the atom.
C) The magnetic field around the atom.
D) The shape of the electron's orbit.
7. The energy of a photon emitted or absorbed during a transition between two energy levels E_i and E_f is given by:|E_f - E_i|. The Bohr model states that this energy difference must be:
A) Zero
B) A continuous range of values
C) Quantized in multiples of hν
D) Equal to the Planck's constant.
8. The Bohr model postulates that electrons revolve around the nucleus in specific orbits without losing energy. These orbits are called:
A) Elliptical orbits
B) Orbitals
C) Stationary states
D) Random paths
9. Which of the following transitions will result in the emission of the highest energy photon?
A) n=2 to n=1
B) n=3 to n=2
C) n=4 to n=3
D) n=5 to n=4
10. The radius of the second Bohr orbit (n=2) is how many times the radius of the first Bohr orbit (n=1)?
A) 2 times
B) 4 times
C) 1/2 times
D) 1/4 times
11. In the Bohr model, the total energy of an electron in the nth orbit is the sum of its kinetic and potential energies. This total energy is proportional to:
A) 1/n²
B) n²
C) 1/n
D) n
12. The potential energy of an electron in the nth Bohr orbit of hydrogen is proportional to:
A) 1/n²
B) n²
C) 1/n
D) n
13. The kinetic energy of an electron in the nth Bohr orbit of hydrogen is proportional to:
A) 1/n²
B) n²
C) 1/n
D) n
14. What is the wave number (1/λ) of the spectral line emitted when an electron transitions from n=3 to n=2 in hydrogen?
A) R_H (1/2² - 1/3²)
B) R_H (1/3² - 1/2²)
C) R_H (1/2² + 1/3²)
D) R_H (1/3² + 1/2²)
15. The Bohr radius (a_0) is approximately:
A) 5.29 x 10⁻¹¹ m
B) 5.29 x 10⁻¹⁰ m
C) 5.29 x 10⁻¹² m
D) 5.29 x 10⁻⁹ m
16. The energy of the second excited state (n=3) of a hydrogen atom is:
A) -13.6 eV
B) -3.4 eV
C) -1.51 eV
D) -0.85 eV
17. What is the relationship between the energy of a photon and its frequency (ν)?
A) E = h/ν
B) E = hν
C) E = ν/h
D) E = h + ν
18. The spectral lines in the Pfund series of hydrogen correspond to transitions to which principal quantum number?
A) n=2
B) n=3
C) n=4
D) n=5
19. The energy required to excite a hydrogen atom from n=1 to n=3 is:
A) 13.6 eV
B) 10.2 eV
C) 12.09 eV
D) 13.05 eV
20. The Bohr model fails to explain the spectra of:
A) Monatomic gases
B) Diatomic molecules
C) Atoms with more than one electron
D) All of the above
21. A transition from n=5 to n=2 in hydrogen atom would result in the emission of a photon in which region?
A) Ultraviolet
B) Visible
C) Infrared
D) Microwave
22. The energy of the emitted photon is equal to the difference in energy between:
A) The initial and final orbits.
B) The nucleus and the electron.
C) The ground state and the excited state.
D) The excited state and the ionization energy.
23. The constant α in the velocity formula v_n = (cα)/n is known as:
A) Rydberg constant
B) Planck constant
C) Fine-structure constant
D) Bohr radius
24. What is the velocity of an electron in the nth Bohr orbit of a hydrogen atom?
A) v_n = (cα)/n
B) v_n = (cα)/n²
C) v_n = cα * n
D) v_n = cα * n²
25. The angular momentum of an electron in the second orbit (n=2) of hydrogen is:
A) h/π
B) 2h/π
C) h/2π
D) 4h/π
26. Which spectral series of hydrogen is observed when electrons transition from higher states to n=4?
A) Lyman
B) Balmer
C) Paschen
D) Brackett
27. The Bohr model is a semi-classical model because:
A) It uses only classical physics.
B) It uses only quantum mechanics.
C) It combines classical concepts (like orbits) with quantum postulates (like quantized energy).
D) It is completely inaccurate.
28. If the electron in a hydrogen atom jumps from n=∞ to n=1, the energy absorbed is:
A) Zero
B) 13.6 eV
C) Infinite
D) Negative
29. The frequency of the emitted radiation during an electronic transition is proportional to:
A) The difference in energy between the two levels.
B) The sum of the energies of the two levels.
C) The energy of the initial level.
D) The energy of the final level.
30. What is the radius of the nth orbit in a hydrogen atom, given by the Bohr model?
A) r_n = a_0 * n²
B) r_n = a_0 / n²
C) r_n = a_0 * n
D) r_n = a_0 / n
31. Which of the following quantities is quantized in the Bohr model?
A) Energy
B) Angular momentum
C) Radius of orbit
D) All of the above
32. The Bohr model successfully explained the spectrum of:
A) Hydrogen atom only
B) Helium atom
C) Lithium atom
D) All atoms with one electron
33. If an electron in a hydrogen atom is in the n=3 state, it can emit photons corresponding to transitions to which lower states?
A) n=1 only
B) n=2 only
C) n=1 and n=2
D) n=4
34. What is the ionization energy of a hydrogen atom in its ground state, according to the Bohr model?
A) 13.6 eV
B) 3.4 eV
C) 1.51 eV
D) 0.85 eV
35. The ionization energy of hydrogen is the energy required to transition an electron from:
A) n=1 to n=2
B) n=1 to n=3
C) n=1 to n=∞
D) n=2 to n=1
36. Which spectral series of hydrogen is observed in the infrared region?
A) Lyman series
B) Balmer series
C) Paschen series
D) Brackett series
37. The Balmer series of the hydrogen spectrum lies in which region of the electromagnetic spectrum?
A) Infrared
B) Visible
C) Ultraviolet
D) X-ray
38. The Lyman series of the hydrogen spectrum corresponds to transitions from higher energy levels to which principal quantum number?
A) n=1
B) n=2
C) n=3
D) n=4
39. What does R_H represent in the Rydberg formula for hydrogen's spectral lines?
A) The Bohr radius
B) The Planck constant
C) The Rydberg constant
D) The frequency of the emitted photon
40. The energy of the emitted photon when an electron transitions from n_i to n_f is given by:
A) E = hν = R_H (1/n_f² - 1/n_i²)
B) E = hν = R_H (1/n_i² - 1/n_f²)
C) E = hν = R_H (n_i² - n_f²)
D) E = hν = R_H (n_f² - n_i²)
41. The transition of an electron from a higher energy level (n_i) to a lower energy level (n_f) results in:
A) Absorption of a photon
B) Emission of a photon
C) No energy change
D) Ionization of the atom
42. Which phenomenon is explained by the Bohr model and leads to the characteristic spectral lines of hydrogen?
A) Electron diffraction
B) Photoelectric effect
C) Emission and absorption of photons
D) Nuclear fusion
43. What happens to the energy of an electron as it moves to a higher energy level (larger n) in a hydrogen atom?
A) It decreases and becomes more negative.
B) It increases and becomes less negative (closer to zero).
C) It remains constant.
D) It becomes zero.
44. The energy of an electron in the nth orbit of a hydrogen atom is given by E_n = -13.6/n² eV. What is the energy of the electron in the ground state (n=1)?
A) -13.6 eV
B) -3.4 eV
C) -1.51 eV
D) -0.85 eV
45. What is the radius of the first Bohr orbit (n=1) for the hydrogen atom?
A) 0.529 Å
B) 1.058 Å
C) 0.265 Å
D) 5.29 Å
46. What does the symbol 'n' represent in the Bohr model's energy level formula (E = -13.6/n² eV)?
A) The principal quantum number
B) The azimuthal quantum number
C) The magnetic quantum number
D) The spin quantum number
47. The energy levels in a hydrogen atom, according to Bohr's model, are quantized. This means:
A) Electrons can have any energy value.
B) Electrons can only possess discrete, specific energy values.
C) Energy is continuously emitted by the electron.
D) Energy is absorbed only when the electron falls to a lower level.
48. What is the unit of angular momentum for an electron in a Bohr orbit?
A) h/2π
B) nh/2π
C) nh
D) h/π
49. According to the Bohr model, when does an electron emit or absorb energy?
A) When it moves between orbits.
B) When it stays in a particular orbit.
C) When it collides with another electron.
D) When it is attracted to the nucleus.
50. What is the fundamental assumption of Bohr's atomic model regarding electron orbits?
A) Electrons can orbit the nucleus at any distance.
B) Electrons orbit the nucleus only in specific, quantized energy levels.
C) Electrons move in random paths around the nucleus.
D) Electrons are stationary at fixed positions around the nucleus.
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