Rutherford scattering and Bohr model of the atom - Question Bank

1. Bohr's model is a semi-classical model because:
A) It uses classical mechanics for orbits but quantum rules for energy.
B) It uses classical electromagnetism for radiation but quantum rules for orbits.
C) It uses classical concepts of force and motion throughout.
D) It is based entirely on quantum principles.
2. The Bohr radius (a₀) is defined as the radius of the ground state orbit of hydrogen. Its value is approximately:
A) 0.53 cm
B) 0.53 mm
C) 0.53 μm
D) 0.53 Å
3. Which of the following quantities is conserved in Rutherford scattering?
A) Linear momentum
B) Angular momentum
C) Kinetic energy
D) All of the above
4. In Rutherford scattering, the number of particles scattered through an angle θ is proportional to:
A) 1/sin(θ/2)
B) 1/sin²(θ/2)
C) 1/sin⁴(θ/2)
D) sin²(θ/2)
5. The energy levels of a hydrogen atom are given by E_n = -13.6/n² eV. What is the energy required to excite an electron from the n=2 state to the n=4 state?
A) 13.6 eV
B) 10.2 eV
C) 3.4 eV
D) 2.55 eV
6. Bohr's model could not explain the relative intensities of spectral lines because:
A) It did not consider the wave nature of electrons.
B) It did not provide a mechanism for radiative transitions.
C) It assumed electrons orbit in fixed paths.
D) It did not account for the Zeeman effect.
7. The ratio of the radius of the nth orbit to the radius of the mth orbit in a hydrogen atom is:
A) n²/m²
B) m²/n²
C) n/m
D) m/n
8. In Bohr's model, the frequency of revolution of an electron in the nth orbit is proportional to:
A) n²/Z²
B) Z²/n³
C) n³/Z²
D) Z²/n²
9. Which spectral series of hydrogen lies in the infrared region?
A) Lyman series
B) Balmer series
C) Paschen series
D) Brackett series
10. The angular momentum of an electron in the first Bohr orbit (n=1) of hydrogen is:
A) h
B) h/2
C) h/2π
D) 2πh
11. If the kinetic energy of an alpha particle is K, and it is directed towards a nucleus of charge Ze, the maximum kinetic energy it can lose at the point of closest approach (head-on collision) is:
A) K
B) K/2
C) 0
D) Ze²/4πε₀K
12. Bohr's model is based on the postulates derived from:
A) Classical physics only
B) Quantum mechanics only
C) A combination of classical physics and quantum postulates
D) Relativity
13. Rutherford's model is also known as the:
A) Planetary model
B) Shell model
C) Quantum model
D) Wave model
14. The total number of spectral lines observed when electrons transition from n=5 to the ground state (n=1) in a sample of hydrogen atoms is:
A) 5
B) 10
C) 15
D) 20
15. The transition from n=∞ to n=1 in a hydrogen atom corresponds to the emission of a photon of energy:
A) 13.6 eV
B) 10.2 eV
C) 3.4 eV
D) 0 eV
16. What is the velocity of an electron in the nth Bohr orbit of hydrogen?
A) v_n ∝ n/Z
B) v_n ∝ Z/n
C) v_n ∝ n²/Z²
D) v_n ∝ Z²/n²
17. Bohr's model introduced the concept of quantization of:
A) Energy only
B) Angular momentum only
C) Both energy and angular momentum
D) Linear momentum
18. In Rutherford scattering, if the energy of the incident alpha particle is E, the cross-section for scattering at angle θ is proportional to:
A) E² sin⁴(θ/2)
B) E sin²(θ/2)
C) 1 / (E² sin⁴(θ/2))
D) 1 / (E sin²(θ/2))
19. The energy of the electron in the second excited state (n=3) of hydrogen atom is:
A) -13.6 eV
B) -3.4 eV
C) -1.51 eV
D) -0.85 eV
20. If the radius of the first Bohr orbit is R₀, then the radius of the second Bohr orbit of hydrogen is:
A) R₀/4
B) R₀/2
C) 2R₀
D) 4R₀
21. According to Bohr's postulate, an electron does not radiate energy while revolving in a stationary orbit because:
A) The orbit is elliptical.
B) The electron is in a state of constant acceleration.
C) The angular momentum is quantized.
D) The orbit is a stable, non-radiating state.
22. The de Broglie wavelength associated with an electron in the nth Bohr orbit of hydrogen is proportional to:
A) n
B) 1/n
C) n²
D) 1/n²
23. Bohr's model is not applicable to:
A) Hydrogen atom
B) Helium ion (He+)
C) Lithium ion (Li++)
D) Atoms with more than one electron
24. In Rutherford scattering, the number of scattered alpha particles detected at an angle θ is proportional to:
A) sin⁴(θ/2)
B) cos⁴(θ/2)
C) 1/sin⁴(θ/2)
D) 1/cos⁴(θ/2)
25. What is the angular frequency of revolution of an electron in the nth Bohr orbit of hydrogen?
A) ω ∝ n² / Z²
B) ω ∝ Z² / n³
C) ω ∝ n³ / Z²
D) ω ∝ Z² / n²
26. If an electron in a hydrogen atom is in the n=4 state, how many different wavelengths of photons can be emitted as it transitions to lower energy states?
A) 3
B) 4
C) 6
D) 10
27. The Pfund series of spectral lines for hydrogen corresponds to transitions from higher energy levels to which principal quantum number level?
A) n=1
B) n=2
C) n=3
D) n=5
28. The Balmer series of spectral lines for hydrogen corresponds to transitions from higher energy levels to which principal quantum number level?
A) n=1
B) n=2
C) n=3
D) n=4
29. Which of the following transitions in a hydrogen atom will emit a photon in the ultraviolet region of the electromagnetic spectrum?
A) n=2 to n=1
B) n=3 to n=2
C) n=4 to n=3
D) n=5 to n=4
30. For a hydrogen-like atom with atomic number Z, the energy of the nth orbit is given by:
A) E_n = -13.6 Z²/n² eV
B) E_n = -13.6 n²/Z² eV
C) E_n = -13.6 Z/n eV
D) E_n = -13.6 n/Z eV
31. In the Bohr model, for a hydrogen-like atom (atomic number Z), the radius of the nth orbit is given by:
A) r_n = a₀ (n²/Z)
B) r_n = a₀ (Z²/n)
C) r_n = a₀ (n/Z²)
D) r_n = a₀ (Z/n²)
32. The ionization energy of hydrogen is the energy required to excite the electron from the ground state (n=1) to the state where it is free from the nucleus (n=∞). Its value is:
A) 13.6 eV
B) -13.6 eV
C) 0 eV
D) 3.4 eV
33. What is the ground state energy of a hydrogen atom according to Bohr's model?
A) -13.6 eV
B) +13.6 eV
C) 0 eV
D) -1.36 eV
34. Bohr's model successfully explained:
A) The fine structure of spectral lines
B) The intensity of spectral lines
C) The discrete line spectrum of hydrogen
D) The scattering of alpha particles
35. The energy difference between two adjacent Bohr orbits is related to the frequency (ν) of the emitted or absorbed photon by:
A) ΔE = hν
B) ΔE = ν/h
C) ΔE = h/ν
D) ΔE = h^2ν
36. When an electron jumps from a higher energy orbit to a lower energy orbit, the atom:
A) Absorbs energy
B) Emits energy in the form of a photon
C) Remains in a stationary state
D) Changes its angular momentum by h/2π
37. For a hydrogen atom, the radius of the first Bohr orbit (n=1) is approximately 0.53 Å. What is the radius of the third Bohr orbit (n=3)?
A) 0.18 Å
B) 1.59 Å
C) 4.77 Å
D) 16.2 Å
38. The radius of the nth orbit in Bohr's model for a hydrogen atom is proportional to:
A) n
B) 1/n
C) n^2
D) 1/n^2
39. In Bohr's model, the energy of an electron in the nth orbit of a hydrogen atom is proportional to:
A) n
B) 1/n
C) n^2
D) 1/n^2
40. Bohr's quantization condition states that the angular momentum (L) of an electron in a stationary orbit is quantized. It is given by:
A) L = mvr = nh
B) L = mvr = n(h/2π)
C) L = mvr = nh/2
D) L = mvr = n(2π/h)
41. According to Bohr's model, electrons revolve around the nucleus in:
A) Any arbitrary orbit
B) Elliptical orbits
C) Specific, stable, non-radiating orbits called stationary states
D) Orbits that continuously change their energy
42. Rutherford's model of the atom failed to explain:
A) The existence of a nucleus
B) The scattering of alpha particles
C) The stability of the atom
D) The quantization of energy levels
43. For a large impact parameter in Rutherford scattering, the deflection angle is:
A) Close to 180 degrees
B) Close to 90 degrees
C) Close to 0 degrees
D) Undefined
44. What is the impact parameter (b) in Rutherford scattering?
A) The distance of closest approach.
B) The perpendicular distance between the initial velocity vector of the alpha particle and the center of the nucleus.
C) The angle of deflection of the alpha particle.
D) The radius of the gold foil.
45. If the kinetic energy of the alpha particle is doubled, the distance of closest approach in Rutherford scattering will:
A) Increase by a factor of 2
B) Decrease by a factor of 2
C) Increase by a factor of sqrt(2)
D) Decrease by a factor of sqrt(2)
46. The distance of closest approach in Rutherford scattering is the minimum distance between the alpha particle and the target nucleus when the alpha particle is directed head-on towards the nucleus. This distance is proportional to:
A) The kinetic energy of the alpha particle
B) The square of the kinetic energy of the alpha particle
C) The inverse of the kinetic energy of the alpha particle
D) The inverse square of the kinetic energy of the alpha particle
47. What did Rutherford's experiment conclude about the positive charge in an atom?
A) It is spread uniformly throughout the atom.
B) It is concentrated in a very small region at the center.
C) It is balanced by an equal amount of negative charge spread evenly.
D) It resides primarily in the electrons.
48. The most significant observation in Rutherford's alpha particle scattering experiment was:
A) Most alpha particles passed through the foil undeflected.
B) A small fraction of alpha particles were deflected by large angles.
C) A very small fraction of alpha particles bounced back.
D) All of the above.
49. According to Rutherford's atomic model, the atom is mostly:
A) Solid and dense
B) Empty space with a small, dense nucleus
C) Composed of uniformly distributed positive charge
D) A cloud of electrons with no central core
50. In Rutherford's scattering experiment, alpha particles are bombarded on a thin gold foil. What is the primary reason for the deflection of alpha particles?
A) Interaction with electrons in the gold foil
B) Interaction with the nucleus of the gold atoms
C) Coulomb repulsion between alpha particles and neighboring foil atoms
D) Scattering due to the magnetic field of the foil
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