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1. Rutherford's alpha-particle scattering experiment led to the discovery of the:
A. Electron
B. Small, dense, positively charged nucleus at the centre of the atom
C. Neutron
D. Proton
Answer: B. Small, dense, positively charged nucleus at the centre of the atom
Explanation: The unexpected large-angle scattering of alpha particles in Rutherford's experiment indicated that an atom's positive charge and most of its mass are concentrated in a tiny, dense central nucleus.
2. According to Rutherford's model, electrons in an atom:
A. Are embedded in a uniform sphere of positive charge
B. Revolve around the nucleus in circular orbits, held by electrostatic attraction
C. Do not exist
D. Are located inside the nucleus
Answer: B. Revolve around the nucleus in circular orbits, held by electrostatic attraction
Explanation: Rutherford's nuclear model proposed that negatively charged electrons revolve in circular orbits around a small, dense, positively charged nucleus, similar to planets around the Sun.
3. Bohr's first postulate about atomic orbits states that the angular momentum of an electron is quantized as:
A. mvr = nh/2π
B. mvr = nh
C. mvr = h/2πn
D. mvr = 2πn/h
Answer: A. mvr = nh/2π
Explanation: Bohr postulated that electrons can revolve only in those orbits where their orbital angular momentum is an integral multiple of h/2π, i.e., mvr = nh/2π, where n is a positive integer.
4. The energy of an electron in the nth orbit of a hydrogen atom is given by:
A. En = −13.6/n eV
B. En = −13.6/n² eV
C. En = 13.6n² eV
D. En = −13.6n eV
Answer: B. En = −13.6/n² eV
Explanation: For the hydrogen atom, the allowed energy levels are quantized and given by En = −13.6/n² eV, where n is the principal quantum number of the orbit.
5. The energy of a hydrogen atom in its ground state (n = 1) is:
A. 0 eV
B. −13.6 eV
C. +13.6 eV
D. −3.4 eV
Answer: B. −13.6 eV
Explanation: Substituting n = 1 into En = −13.6/n² eV gives the ground state energy of the hydrogen atom as exactly −13.6 eV, its lowest (most stable) energy level.
6. The Lyman series of hydrogen spectral lines lies in which region?
A. Infrared
B. Visible
C. Ultraviolet
D. X-ray
Answer: C. Ultraviolet
Explanation: The Lyman series, resulting from electron transitions to the n = 1 level, involves relatively large energy differences and hence falls in the ultraviolet region of the spectrum.
7. The Balmer series of hydrogen spectral lines, which lies mostly in the visible region, corresponds to transitions ending at:
A. n = 1
B. n = 2
C. n = 3
D. n = infinity
Answer: B. n = 2
Explanation: The Balmer series arises from electron transitions from higher energy levels down to the n = 2 level, and its spectral lines fall largely within the visible range of light.
8. The ionization energy of a hydrogen atom from its ground state is:
A. 3.4 eV
B. 13.6 eV
C. 1.5 eV
D. 0.85 eV
Answer: B. 13.6 eV
Explanation: Ionization energy is the energy required to remove the electron completely from the ground state (n=1, energy −13.6 eV) to n = infinity (energy 0), which equals 13.6 eV.
9. De Broglie's hypothesis provided a physical explanation for Bohr's quantization condition by proposing that:
A. Electrons behave purely as particles
B. Stationary orbits are those which contain a whole number of electron de Broglie wavelengths
C. Electrons have no wave nature
D. The nucleus emits matter waves
Answer: B. Stationary orbits are those which contain a whole number of electron de Broglie wavelengths
Explanation: De Broglie showed that Bohr's allowed orbits correspond exactly to those in which an integral number of the electron's de Broglie wavelengths fit along the orbit's circumference, forming a standing wave.
10. The radius of the nth orbit in the Bohr model varies with n as:
A. rn ∝ n
B. rn ∝ n²
C. rn ∝ 1/n
D. rn ∝ 1/n²
Answer: B. rn ∝ n²
Explanation: According to the Bohr model, the radius of an electron's orbit increases with the square of the principal quantum number, i.e., rn = n² r1, where r1 is the Bohr radius.
11. The speed of an electron in the nth Bohr orbit varies with n as:
A. vn ∝ n
B. vn ∝ n²
C. vn ∝ 1/n
D. vn is independent of n
Answer: C. vn ∝ 1/n
Explanation: In the Bohr model, the orbital speed of the electron is inversely proportional to the principal quantum number, vn ∝ 1/n, so electrons move slower in higher orbits.
12. A continuous spectrum differs from a line spectrum in that a continuous spectrum:
A. Contains all wavelengths without gaps, unlike distinct sharp lines of a line spectrum
B. Is emitted only by gases
C. Has no relation to energy transitions
D. Is produced only by hydrogen
Answer: A. Contains all wavelengths without gaps, unlike distinct sharp lines of a line spectrum
Explanation: A continuous spectrum consists of an unbroken range of wavelengths (as from a hot solid or dense gas), whereas a line spectrum has sharp, discrete lines corresponding to specific energy transitions in atoms.
13. A major limitation of the Bohr model is that it:
A. Could not explain the spectrum of hydrogen at all
B. Could not satisfactorily explain the spectra of multi-electron atoms and fine spectral structure
C. Predicted incorrect energy for the hydrogen ground state
D. Contradicted Rutherford's experiment
Answer: B. Could not satisfactorily explain the spectra of multi-electron atoms and fine spectral structure
Explanation: While the Bohr model successfully explained the hydrogen spectrum, it failed to accurately account for the spectra of atoms with more than one electron and could not explain finer spectral details.
14. The impact parameter in Rutherford scattering is defined as:
A. The closest distance of approach of the alpha particle to the nucleus
B. The perpendicular distance between the initial velocity vector of the alpha particle and the center of the nucleus
C. The mass of the alpha particle
D. The scattering angle
Answer: B. The perpendicular distance between the initial velocity vector of the alpha particle and the center of the nucleus
Explanation: Impact parameter is the perpendicular distance from the nucleus to the original straight-line path of the incoming alpha particle if there were no force of interaction.
15. The distance of closest approach of an alpha particle to the nucleus in Rutherford's experiment gives an estimate of:
A. The size of the electron
B. An upper limit on the size of the nucleus
C. The mass of the atom
D. The wavelength of the alpha particle
Answer: B. An upper limit on the size of the nucleus
Explanation: At the distance of closest approach, all kinetic energy of the alpha particle converts to electrostatic potential energy, allowing an estimate of the upper limit of the nuclear size.
16. In Rutherford's alpha scattering experiment, the observation that most alpha particles passed through the gold foil almost undeflected indicated that:
A. Atoms are mostly empty space
B. Atoms are solid throughout
C. The nucleus is very large
D. Electrons are heavier than the nucleus
Answer: A. Atoms are mostly empty space
Explanation: Since the vast majority of alpha particles passed through with little to no deflection, it implied that most of the volume of an atom is empty space, with a tiny dense nucleus at its center.
17. The frequency of radiation emitted when an electron jumps from a higher energy level Ei to a lower energy level Ef is given by:
A. ν = (Ei − Ef)/h
B. ν = (Ei + Ef)/h
C. ν = h(Ei − Ef)
D. ν = Ei/Ef
Answer: A. ν = (Ei − Ef)/h
Explanation: By Bohr's frequency condition, the emitted photon's frequency is proportional to the energy difference between the initial and final orbits, ν = (Ei − Ef)/h.
18. Which of the following spectral series of hydrogen lies in the infrared region?
A. Lyman series
B. Balmer series
C. Paschen series
D. None of these
Answer: C. Paschen series
Explanation: The Paschen series, resulting from transitions ending at n = 3, involves smaller energy differences and its spectral lines lie in the infrared region.
19. In Bohr's model, as the principal quantum number n increases, the energy levels of the hydrogen atom become:
A. Farther apart
B. Closer together, approaching zero
C. Exactly equal
D. Negative infinity
Answer: B. Closer together, approaching zero
Explanation: Since En = −13.6/n² eV, as n increases the energy levels rise (become less negative) and get progressively closer together, converging towards zero at n = infinity (ionization).
20. Excitation energy of an atom refers to the energy required to:
A. Completely remove an electron from the atom
B. Raise an electron from a lower energy state to a specified higher energy state
C. Fuse two nuclei
D. Split the nucleus
Answer: B. Raise an electron from a lower energy state to a specified higher energy state
Explanation: Excitation energy is the energy that must be supplied to move an electron from its current (often ground) energy level up to a higher, specified energy level within the same atom.
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