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Bohr model, orbit energy/radius relations and limitations: NEET MCQs with answers

68 questions on this topic of Atomic Structure (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.

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easy

1. Which of the following is a fundamental limitation of Bohr's atomic model when compared to modern quantum mechanics?

  1. It fails to explain the conservation of energy during electronic transitions.
  2. It treats an electron as a particle with well-defined position and momentum, contradicting Heisenberg's uncertainty principle.
  3. It assumes that electrostatic forces obey Coulomb's inverse-square law.
  4. It predicts continuous rather than discrete energy states for one-electron systems.
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Answer: (B) It treats an electron as a particle with well-defined position and momentum, contradicting Heisenberg's uncertainty principle.

Bohr assumed electrons move in definite circular orbits with fixed radii and velocities, which implies simultaneous exact knowledge of position and momentum. This directly violates Heisenberg's uncertainty principle (Δx · Δp ≥ h / 4π).

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2. The radius of the third Bohr orbit of He⁺ is (a₀ = 0.529 Å):

  1. 0.794 Å
  2. 4.76 Å
  3. 2.38 Å
  4. 9.52 Å
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Answer: (C) 2.38 Å

rₙ = 0.529 n²/Z Å = 0.529 × 3²/2 = 2.38 Å.

hard

3. The speed of an electron in the nth Bohr orbit of a hydrogen atom is vₙ and the radius of the orbit is rₙ. If a graph is plotted taking log(vₙ) on the y-axis and log(rₙ) on the x-axis, the slope of the resulting straight line is:

  1. -0.5
  2. -2
  3. -1
  4. +0.5
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Answer: (A) -0.5

For a hydrogen atom, vₙ ∝ 1/n and rₙ ∝ n². This means n ∝ rₙ^(1/2). Substituting this into the velocity proportionality gives vₙ ∝ 1 / (rₙ^(1/2)) = rₙ^(-1/2). Taking logarithms on both sides: log(vₙ) = -0.5 log(rₙ) + constant. Therefore, the slope of the log(vₙ) versus log(rₙ) graph is -0.5.

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4. In a hydrogen atom, an electron absorbs energy and jumps to an orbit such that its radius increases by a factor of 16 compared to its ground state radius. The ratio of the orbital frequency in the initial orbit to that in the final orbit is:

  1. 64 : 1
  2. 16 : 1
  3. 4 : 1
  4. 256 : 1
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Answer: (A) 64 : 1

Orbital radius scales as r ∝ n². Since r_final / r_initial = 16, n_final / n_initial = √16 = 4. The frequency of revolution is f ∝ 1 / n³. Hence, f_initial / f_final = (n_final / n_initial)³ = 4³ = 64 : 1.

easy

5. The splitting of spectral lines of hydrogen-like species in the presence of an external magnetic field is known as the Zeeman effect. Which of the following is the primary reason why Bohr's model fails to explain this effect?

  1. It assumes an electron revolves in elliptical paths.
  2. It violates the law of conservation of angular momentum.
  3. It does not incorporate the wave nature and spin magnetic moment of the electron in three dimensions.
  4. It predicts zero orbital angular momentum for all ground-state electrons.
Show answer and explanation

Answer: (C) It does not incorporate the wave nature and spin magnetic moment of the electron in three dimensions.

Bohr's theory restricts electron motion to two-dimensional planar circular orbits with quantization rule mvr = nh/(2π). It fails to account for three-dimensional wave nature, space quantization, and the electron's intrinsic magnetic moment (spin), which are required to explain the Zeeman and Stark effects.

hard

6. In a collection of Li²⁺ ions in a certain excited state 'n', the radius of the orbit is 3 times the radius of the ground state of a hydrogen atom. What is the total energy of an electron in this orbit of Li²⁺?

  1. -4.53 eV
  2. -40.8 eV
  3. -13.6 eV
  4. -1.51 eV
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Answer: (C) -13.6 eV

Radius is given by r = a₀ (n² / Z). For Li²⁺, Z = 3, so r = a₀ (n² / 3). Given r = 3 a₀, we have n² / 3 = 3 ⇒ n² = 9, so n = 3. The total energy of an electron in this orbit is E₃ = -13.6 × (Z² / n²) eV = -13.6 × (3² / 3²) = -13.6 eV.

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7. The energy of the electron in the n = 3 orbit of Li²⁺ is:

  1. 13.6 eV
  2. −4.53 eV
  3. −13.6 eV
  4. −1.51 eV
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Answer: (C) −13.6 eV

Eₙ = −13.6 Z²/n² eV = −13.6 × 3²/3² = −13.6 eV.

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8. The radius of the fourth Bohr orbit of Li²⁺ is (a₀ = 0.529 Å):

  1. 25.4 Å
  2. 2.82 Å
  3. 8.46 Å
  4. 0.705 Å
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Answer: (B) 2.82 Å

rₙ = 0.529 n²/Z Å = 0.529 × 4²/3 = 2.82 Å.

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9. The ratio of the acceleration of an electron in the first Bohr orbit of a hydrogen atom to that in the second Bohr orbit of a He⁺ ion is:

  1. 8 : 1
  2. 1 : 1
  3. 4 : 1
  4. 2 : 1
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Answer: (D) 2 : 1

Acceleration of an electron in an orbit is given by a = v² / r. Since v ∝ Z / n and r ∝ n² / Z, we have a ∝ Z³ / n⁴. For H (Z = 1, n = 1), a₁ ∝ 1³ / 1⁴ = 1. For He⁺ (Z = 2, n = 2), a₂ ∝ 2³ / 2⁴ = 8 / 16 = 1/2. Therefore, the ratio a₁ : a₂ = 1 : (1/2) = 2 : 1.

easy

10. According to Bohr's theory, which of the following quantities decreases as the principal quantum number (n) increases for a given hydrogen atom?

  1. Orbital radius
  2. Kinetic energy of the electron
  3. Orbital time period
  4. Potential energy of the electron
Show answer and explanation

Answer: (B) Kinetic energy of the electron

Kinetic energy K = 13.6 / n² eV, which decreases as n increases. Orbital radius r ∝ n² (increases), orbital period T ∝ n³ (increases), and potential energy U = -27.2 / n² eV becomes less negative, meaning it increases.

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11. The radius of the third Bohr orbit of H is (a₀ = 0.529 Å):

  1. 4.76 Å
  2. 1.59 Å
  3. 2.38 Å
  4. 9.52 Å
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Answer: (A) 4.76 Å

rₙ = 0.529 n²/Z Å = 0.529 × 3²/1 = 4.76 Å.

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12. For a hydrogen-like species of atomic number Z, the linear momentum (p) of an electron revolving in the nth Bohr orbit is proportional to:

  1. n / Z
  2. Z² / n
  3. Z / n²
  4. Z / n
Show answer and explanation

Answer: (D) Z / n

Linear momentum is p = mv. Since mass m is constant and the orbital velocity v ∝ Z / n in Bohr's model, the linear momentum p is directly proportional to Z / n.

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