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NCERT Solutions › Physics › Chapter 12

Chapter 12: Atoms

NCERT Solutions for CBSE Class 10 Physics — 79 solved questions with detailed explanations.

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Solved Questions

Q1. In Bohr's model, the radius of the nth orbit is proportional to:

Difficulty: Easy · Topic: Bohr Model

Solution

r_n = a₀ n²/Z. Radius is proportional to n².

Q2. The energy of an electron in the nth orbit of hydrogen atom is:

Difficulty: Easy · Topic: Energy Levels

Solution

E_n = -13.6/n² eV for hydrogen atom.

Q3. Energy of electron in the n=1 orbit of hydrogen is:

Difficulty: Easy-Medium · Topic: Bohr Model

Solution

E_n = -13.6/n² = -13.6/1² = -13.6 eV.

Q4. Energy of electron in the n=2 orbit of hydrogen is:

Difficulty: Easy-Medium · Topic: Bohr Model

Solution

E_n = -13.6/n² = -13.6/2² = -3.4 eV.

Q5. Energy of electron in the n=3 orbit of hydrogen is:

Difficulty: Easy-Medium · Topic: Bohr Model

Solution

E_n = -13.6/n² = -13.6/3² = -1.511 eV.

Q6. Energy of electron in the n=4 orbit of hydrogen is:

Difficulty: Easy-Medium · Topic: Bohr Model

Solution

E_n = -13.6/n² = -13.6/4² = -0.85 eV.

Q7. Energy of electron in the n=5 orbit of hydrogen is:

Difficulty: Easy-Medium · Topic: Bohr Model

Solution

E_n = -13.6/n² = -13.6/5² = -0.544 eV.

Q8. Energy of electron in the n=6 orbit of hydrogen is:

Difficulty: Easy-Medium · Topic: Bohr Model

Solution

E_n = -13.6/n² = -13.6/6² = -0.378 eV.

Q9. Energy of hydrogen electron in n=1 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q10. Energy of hydrogen electron in n=2 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q11. Energy of hydrogen electron in n=3 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q12. Energy of hydrogen electron in n=4 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q13. Energy of hydrogen electron in n=5 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q14. Energy of hydrogen electron in n=6 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q15. Energy of hydrogen electron in n=7 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q16. Energy of hydrogen electron in n=8 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q17. Energy of hydrogen electron in n=9 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q18. Energy of hydrogen electron in n=10 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q19. Energy of hydrogen electron in n=11 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q20. Energy of hydrogen electron in n=12 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q21. Energy of hydrogen electron in n=13 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q22. Energy of hydrogen electron in n=14 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q23. Energy of hydrogen electron in n=15 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q24. Energy of hydrogen electron in n=16 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q25. Energy of hydrogen electron in n=17 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q26. Energy of hydrogen electron in n=18 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q27. Energy of hydrogen electron in n=19 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q28. Energy of hydrogen electron in n=20 orbit is:

Difficulty: Easy-Medium · Topic: Bohr

Solution

En = -13.6/n² eV.

Q29. The wavelength of the first line in the Lyman series of hydrogen is (R = 1.097 × 10⁷ m⁻¹):

Difficulty: Medium · Topic: Hydrogen Spectrum

Solution

1/λ = R(1/1² - 1/2²) = R(3/4). λ = 4/(3R) = 4/(3×1.097×10⁷) = 121.6 nm.

Q30. The wavelength of Lyman series line (n₂=2 → n₁=1) in hydrogen is approximately:

Difficulty: Medium · Topic: Hydrogen Spectrum

Solution

1/λ = R(1/1²-1/2²). λ ≈ 121.5 nm.

Q31. The wavelength of Lyman series line (n₂=3 → n₁=1) in hydrogen is approximately:

Difficulty: Medium · Topic: Hydrogen Spectrum

Solution

1/λ = R(1/1²-1/3²). λ ≈ 102.6 nm.

Q32. The wavelength of Lyman series line (n₂=4 → n₁=1) in hydrogen is approximately:

Difficulty: Medium · Topic: Hydrogen Spectrum

Solution

1/λ = R(1/1²-1/4²). λ ≈ 97.2 nm.

Q33. The wavelength of Balmer series line (n₂=3 → n₁=2) in hydrogen is approximately:

Difficulty: Medium · Topic: Hydrogen Spectrum

Solution

1/λ = R(1/2²-1/3²). λ ≈ 656.3 nm.

Q34. The wavelength of Balmer series line (n₂=4 → n₁=2) in hydrogen is approximately:

Difficulty: Medium · Topic: Hydrogen Spectrum

Solution

1/λ = R(1/2²-1/4²). λ ≈ 486.2 nm.

Q35. The wavelength of Balmer series line (n₂=5 → n₁=2) in hydrogen is approximately:

Difficulty: Medium · Topic: Hydrogen Spectrum

Solution

1/λ = R(1/2²-1/5²). λ ≈ 434.1 nm.

Q36. The wavelength of Paschen series line (n₂=4 → n₁=3) in hydrogen is approximately:

Difficulty: Medium · Topic: Hydrogen Spectrum

Solution

1/λ = R(1/3²-1/4²). λ ≈ 1875.2 nm.

Q37. The wavelength of Paschen series line (n₂=5 → n₁=3) in hydrogen is approximately:

Difficulty: Medium · Topic: Hydrogen Spectrum

Solution

1/λ = R(1/3²-1/5²). λ ≈ 1281.9 nm.

Q38. The wavelength of Paschen series line (n₂=6 → n₁=3) in hydrogen is approximately:

Difficulty: Medium · Topic: Hydrogen Spectrum

Solution

1/λ = R(1/3²-1/6²). λ ≈ 1093.9 nm.

Q39. H-atom transition n=2→n=1. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/1²-1/2²)=10.2 eV.

Q40. H-atom transition n=2→n=1. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/10.2=121.6 nm.

Q41. H-atom transition n=3→n=1. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/1²-1/3²)=12.089 eV.

Q42. H-atom transition n=3→n=1. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/12.089=102.6 nm.

Q43. H-atom transition n=4→n=1. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/1²-1/4²)=12.75 eV.

Q44. H-atom transition n=4→n=1. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/12.75=97.3 nm.

Q45. H-atom transition n=5→n=1. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/1²-1/5²)=13.056 eV.

Q46. H-atom transition n=5→n=1. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/13.056=95.0 nm.

Q47. H-atom transition n=6→n=1. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/1²-1/6²)=13.222 eV.

Q48. H-atom transition n=6→n=1. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/13.222=93.8 nm.

Q49. H-atom transition n=7→n=1. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/1²-1/7²)=13.322 eV.

Q50. H-atom transition n=7→n=1. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/13.322=93.1 nm.

Q51. H-atom transition n=3→n=2. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/2²-1/3²)=1.889 eV.

Q52. H-atom transition n=3→n=2. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/1.889=656.4 nm.

Q53. H-atom transition n=4→n=2. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/2²-1/4²)=2.55 eV.

Q54. H-atom transition n=4→n=2. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/2.55=486.3 nm.

Q55. H-atom transition n=5→n=2. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/2²-1/5²)=2.856 eV.

Q56. H-atom transition n=5→n=2. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/2.856=434.2 nm.

Q57. H-atom transition n=6→n=2. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/2²-1/6²)=3.022 eV.

Q58. H-atom transition n=6→n=2. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/3.022=410.3 nm.

Q59. H-atom transition n=7→n=2. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/2²-1/7²)=3.122 eV.

Q60. H-atom transition n=7→n=2. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/3.122=397.2 nm.

Q61. H-atom transition n=4→n=3. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/3²-1/4²)=0.661 eV.

Q62. H-atom transition n=4→n=3. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/0.661=1875.9 nm.

Q63. H-atom transition n=5→n=3. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/3²-1/5²)=0.967 eV.

Q64. H-atom transition n=5→n=3. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/0.967=1282.3 nm.

Q65. H-atom transition n=6→n=3. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/3²-1/6²)=1.133 eV.

Q66. H-atom transition n=6→n=3. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/1.133=1094.4 nm.

Q67. H-atom transition n=7→n=3. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/3²-1/7²)=1.234 eV.

Q68. H-atom transition n=7→n=3. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/1.234=1004.9 nm.

Q69. H-atom transition n=5→n=4. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/4²-1/5²)=0.306 eV.

Q70. H-atom transition n=5→n=4. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/0.306=4052.3 nm.

Q71. H-atom transition n=6→n=4. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/4²-1/6²)=0.472 eV.

Q72. H-atom transition n=6→n=4. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/0.472=2627.1 nm.

Q73. H-atom transition n=7→n=4. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/4²-1/7²)=0.572 eV.

Q74. H-atom transition n=7→n=4. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/0.572=2167.8 nm.

Q75. H-atom transition n=6→n=5. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/5²-1/6²)=0.166 eV.

Q76. H-atom transition n=6→n=5. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/0.166=7469.9 nm.

Q77. H-atom transition n=7→n=5. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/5²-1/7²)=0.266 eV.

Q78. H-atom transition n=7→n=5. Wavelength(nm):

Difficulty: Medium · Topic: Spectrum

Solution

λ=1240/0.266=4661.7 nm.

Q79. H-atom transition n=7→n=6. Photon energy(eV):

Difficulty: Medium · Topic: Spectrum

Solution

E=13.6(1/6²-1/7²)=0.1 eV.

Other Chapters in Physics

Ch 1: Electric Charges & FieldsCh 2: Electrostatic PotentialCh 3: Current ElectricityCh 4: Moving Charges & MagnetismCh 5: Magnetism & MatterCh 6: Electromagnetic InductionCh 7: Alternating CurrentCh 8: Electromagnetic WavesCh 9: Ray OpticsCh 10: Wave OpticsCh 11: Dual Nature of RadiationCh 13: NucleiCh 14: Semiconductor Electronics

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