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NCERT Solutions › Physics › Chapter 13

Chapter 13: Nuclei

NCERT Solutions for CBSE Class 10 Physics — 105 solved questions with detailed explanations.

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Questions
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Solved Questions

Q1. The binding energy per nucleon is maximum for:

Difficulty: Easy · Topic: Binding Energy

Solution

Iron-56 has the highest binding energy per nucleon (~8.8 MeV), making it the most stable nucleus.

Q2. In β⁻ decay, a neutron converts to:

Difficulty: Easy-Medium · Topic: Radioactive Decay

Solution

n → p + e⁻ + ν̄_e. A neutron decays into a proton, electron, and electron antineutrino.

Q3. The half-life of a radioactive substance is 5 years. The fraction remaining after 15 years is:

Difficulty: Easy-Medium · Topic: Half Life

Solution

15 years = 3 half-lives. Fraction remaining = (1/2)³ = 1/8.

Q4. The mass defect of a nucleus with Z protons and N neutrons is:

Difficulty: Easy-Medium · Topic: Mass Defect

Solution

Δm = Zm_p + Nm_n - M_nucleus. The mass defect equals the difference between sum of constituent masses and actual nuclear mass.

Q5. A substance has half-life 2 years. Fraction remaining after 6 years is:

Difficulty: Easy-Medium · Topic: Half Life

Solution

6/2 = 3 half-lives. Fraction = (1/2)^3 = 1/8.

Q6. A substance has half-life 5 years. Fraction remaining after 15 years is:

Difficulty: Easy-Medium · Topic: Half Life

Solution

15/5 = 3 half-lives. Fraction = (1/2)^3 = 1/8.

Q7. A substance has half-life 10 years. Fraction remaining after 30 years is:

Difficulty: Easy-Medium · Topic: Half Life

Solution

30/10 = 3 half-lives. Fraction = (1/2)^3 = 1/8.

Q8. A substance has half-life 4 years. Fraction remaining after 12 years is:

Difficulty: Easy-Medium · Topic: Half Life

Solution

12/4 = 3 half-lives. Fraction = (1/2)^3 = 1/8.

Q9. A substance has half-life 3 years. Fraction remaining after 9 years is:

Difficulty: Easy-Medium · Topic: Half Life

Solution

9/3 = 3 half-lives. Fraction = (1/2)^3 = 1/8.

Q10. In alpha decay, the mass number decreases by:

Difficulty: Easy-Medium · Topic: Nuclear Physics

Solution

4.

Q11. In alpha decay, the atomic number decreases by:

Difficulty: Easy-Medium · Topic: Nuclear Physics

Solution

2.

Q12. In beta-minus decay, atomic number:

Difficulty: Easy-Medium · Topic: Nuclear Physics

Solution

increases by 1.

Q13. In gamma decay, both A and Z:

Difficulty: Easy-Medium · Topic: Nuclear Physics

Solution

remain unchanged.

Q14. Nuclear fission produces:

Difficulty: Easy-Medium · Topic: Nuclear Physics

Solution

heavier nuclei splitting into lighter.

Q15. Nuclear fusion requires:

Difficulty: Easy-Medium · Topic: Nuclear Physics

Solution

very high temperature.

Q16. Half-life is 2 hours. Fraction remaining after 6 hours is:

Difficulty: Easy-Medium · Topic: Half-Life

Solution

3 half-lives. (1/2)³ = 1/8.

Q17. Half-life is 3 hours. Fraction remaining after 9 hours is:

Difficulty: Easy-Medium · Topic: Half-Life

Solution

3 half-lives. (1/2)³ = 1/8.

Q18. Half-life is 4 hours. Fraction remaining after 12 hours is:

Difficulty: Easy-Medium · Topic: Half-Life

Solution

3 half-lives. (1/2)³ = 1/8.

Q19. Half-life is 5 hours. Fraction remaining after 15 hours is:

Difficulty: Easy-Medium · Topic: Half-Life

Solution

3 half-lives. (1/2)³ = 1/8.

Q20. Half-life is 6 hours. Fraction remaining after 18 hours is:

Difficulty: Easy-Medium · Topic: Half-Life

Solution

3 half-lives. (1/2)³ = 1/8.

Q21. Half-life is 7 hours. Fraction remaining after 21 hours is:

Difficulty: Easy-Medium · Topic: Half-Life

Solution

3 half-lives. (1/2)³ = 1/8.

Q22. Half-life is 8 hours. Fraction remaining after 24 hours is:

Difficulty: Easy-Medium · Topic: Half-Life

Solution

3 half-lives. (1/2)³ = 1/8.

Q23. Half-life is 9 hours. Fraction remaining after 27 hours is:

Difficulty: Easy-Medium · Topic: Half-Life

Solution

3 half-lives. (1/2)³ = 1/8.

Q24. In 9 half-lives, fraction remaining is:

Difficulty: Easy-Medium · Topic: Decay

Solution

(1/2)^9 = 1/512.

Q25. In 10 half-lives, fraction remaining is:

Difficulty: Easy-Medium · Topic: Decay

Solution

(1/2)^10 = 1/1024.

Q26. In 11 half-lives, fraction remaining is:

Difficulty: Easy-Medium · Topic: Decay

Solution

(1/2)^11 = 1/2048.

Q27. In 12 half-lives, fraction remaining is:

Difficulty: Easy-Medium · Topic: Decay

Solution

(1/2)^12 = 1/4096.

Q28. In 13 half-lives, fraction remaining is:

Difficulty: Easy-Medium · Topic: Decay

Solution

(1/2)^13 = 1/8192.

Q29. In 14 half-lives, fraction remaining is:

Difficulty: Easy-Medium · Topic: Decay

Solution

(1/2)^14 = 1/16384.

Q30. In 15 half-lives, fraction remaining is:

Difficulty: Easy-Medium · Topic: Decay

Solution

(1/2)^15 = 1/32768.

Q31. In 16 half-lives, fraction remaining is:

Difficulty: Easy-Medium · Topic: Decay

Solution

(1/2)^16 = 1/65536.

Q32. In 17 half-lives, fraction remaining is:

Difficulty: Easy-Medium · Topic: Decay

Solution

(1/2)^17 = 1/131072.

Q33. In 18 half-lives, fraction remaining is:

Difficulty: Easy-Medium · Topic: Decay

Solution

(1/2)^18 = 1/262144.

Q34. In 19 half-lives, fraction remaining is:

Difficulty: Easy-Medium · Topic: Decay

Solution

(1/2)^19 = 1/524288.

Q35. In 20 half-lives, fraction remaining is:

Difficulty: Easy-Medium · Topic: Decay

Solution

(1/2)^20 = 1/1048576.

Q36. t½=1h. Fraction after 1h:

Difficulty: Easy-Medium · Topic: Decay

Solution

1 half-lives. (1/2)^1=1/2.

Q37. t½=1h. Fraction after 2h:

Difficulty: Easy-Medium · Topic: Decay

Solution

2 half-lives. (1/2)^2=1/4.

Q38. t½=1h. Fraction after 3h:

Difficulty: Easy-Medium · Topic: Decay

Solution

3 half-lives. (1/2)^3=1/8.

Q39. t½=1h. Fraction after 4h:

Difficulty: Easy-Medium · Topic: Decay

Solution

4 half-lives. (1/2)^4=1/16.

Q40. t½=1h. Fraction after 5h:

Difficulty: Easy-Medium · Topic: Decay

Solution

5 half-lives. (1/2)^5=1/32.

Q41. t½=1h. Fraction after 6h:

Difficulty: Easy-Medium · Topic: Decay

Solution

6 half-lives. (1/2)^6=1/64.

Q42. t½=1h. Fraction after 7h:

Difficulty: Easy-Medium · Topic: Decay

Solution

7 half-lives. (1/2)^7=1/128.

Q43. t½=2h. Fraction after 2h:

Difficulty: Easy-Medium · Topic: Decay

Solution

1 half-lives. (1/2)^1=1/2.

Q44. t½=2h. Fraction after 4h:

Difficulty: Easy-Medium · Topic: Decay

Solution

2 half-lives. (1/2)^2=1/4.

Q45. t½=2h. Fraction after 6h:

Difficulty: Easy-Medium · Topic: Decay

Solution

3 half-lives. (1/2)^3=1/8.

Q46. t½=2h. Fraction after 8h:

Difficulty: Easy-Medium · Topic: Decay

Solution

4 half-lives. (1/2)^4=1/16.

Q47. t½=2h. Fraction after 10h:

Difficulty: Easy-Medium · Topic: Decay

Solution

5 half-lives. (1/2)^5=1/32.

Q48. t½=2h. Fraction after 12h:

Difficulty: Easy-Medium · Topic: Decay

Solution

6 half-lives. (1/2)^6=1/64.

Q49. t½=2h. Fraction after 14h:

Difficulty: Easy-Medium · Topic: Decay

Solution

7 half-lives. (1/2)^7=1/128.

Q50. t½=3h. Fraction after 3h:

Difficulty: Easy-Medium · Topic: Decay

Solution

1 half-lives. (1/2)^1=1/2.

Q51. t½=3h. Fraction after 6h:

Difficulty: Easy-Medium · Topic: Decay

Solution

2 half-lives. (1/2)^2=1/4.

Q52. t½=3h. Fraction after 9h:

Difficulty: Easy-Medium · Topic: Decay

Solution

3 half-lives. (1/2)^3=1/8.

Q53. t½=3h. Fraction after 12h:

Difficulty: Easy-Medium · Topic: Decay

Solution

4 half-lives. (1/2)^4=1/16.

Q54. t½=3h. Fraction after 15h:

Difficulty: Easy-Medium · Topic: Decay

Solution

5 half-lives. (1/2)^5=1/32.

Q55. t½=3h. Fraction after 18h:

Difficulty: Easy-Medium · Topic: Decay

Solution

6 half-lives. (1/2)^6=1/64.

Q56. t½=3h. Fraction after 21h:

Difficulty: Easy-Medium · Topic: Decay

Solution

7 half-lives. (1/2)^7=1/128.

Q57. t½=4h. Fraction after 4h:

Difficulty: Easy-Medium · Topic: Decay

Solution

1 half-lives. (1/2)^1=1/2.

Q58. t½=4h. Fraction after 8h:

Difficulty: Easy-Medium · Topic: Decay

Solution

2 half-lives. (1/2)^2=1/4.

Q59. t½=4h. Fraction after 12h:

Difficulty: Easy-Medium · Topic: Decay

Solution

3 half-lives. (1/2)^3=1/8.

Q60. t½=4h. Fraction after 16h:

Difficulty: Easy-Medium · Topic: Decay

Solution

4 half-lives. (1/2)^4=1/16.

Q61. t½=4h. Fraction after 20h:

Difficulty: Easy-Medium · Topic: Decay

Solution

5 half-lives. (1/2)^5=1/32.

Q62. t½=4h. Fraction after 24h:

Difficulty: Easy-Medium · Topic: Decay

Solution

6 half-lives. (1/2)^6=1/64.

Q63. t½=4h. Fraction after 28h:

Difficulty: Easy-Medium · Topic: Decay

Solution

7 half-lives. (1/2)^7=1/128.

Q64. t½=5h. Fraction after 5h:

Difficulty: Easy-Medium · Topic: Decay

Solution

1 half-lives. (1/2)^1=1/2.

Q65. t½=5h. Fraction after 10h:

Difficulty: Easy-Medium · Topic: Decay

Solution

2 half-lives. (1/2)^2=1/4.

Q66. t½=5h. Fraction after 15h:

Difficulty: Easy-Medium · Topic: Decay

Solution

3 half-lives. (1/2)^3=1/8.

Q67. t½=5h. Fraction after 20h:

Difficulty: Easy-Medium · Topic: Decay

Solution

4 half-lives. (1/2)^4=1/16.

Q68. t½=5h. Fraction after 25h:

Difficulty: Easy-Medium · Topic: Decay

Solution

5 half-lives. (1/2)^5=1/32.

Q69. t½=5h. Fraction after 30h:

Difficulty: Easy-Medium · Topic: Decay

Solution

6 half-lives. (1/2)^6=1/64.

Q70. t½=5h. Fraction after 35h:

Difficulty: Easy-Medium · Topic: Decay

Solution

7 half-lives. (1/2)^7=1/128.

Q71. t½=6h. Fraction after 6h:

Difficulty: Easy-Medium · Topic: Decay

Solution

1 half-lives. (1/2)^1=1/2.

Q72. t½=6h. Fraction after 12h:

Difficulty: Easy-Medium · Topic: Decay

Solution

2 half-lives. (1/2)^2=1/4.

Q73. t½=6h. Fraction after 18h:

Difficulty: Easy-Medium · Topic: Decay

Solution

3 half-lives. (1/2)^3=1/8.

Q74. t½=6h. Fraction after 24h:

Difficulty: Easy-Medium · Topic: Decay

Solution

4 half-lives. (1/2)^4=1/16.

Q75. t½=6h. Fraction after 30h:

Difficulty: Easy-Medium · Topic: Decay

Solution

5 half-lives. (1/2)^5=1/32.

Q76. t½=6h. Fraction after 36h:

Difficulty: Easy-Medium · Topic: Decay

Solution

6 half-lives. (1/2)^6=1/64.

Q77. t½=6h. Fraction after 42h:

Difficulty: Easy-Medium · Topic: Decay

Solution

7 half-lives. (1/2)^7=1/128.

Q78. t½=7h. Fraction after 7h:

Difficulty: Easy-Medium · Topic: Decay

Solution

1 half-lives. (1/2)^1=1/2.

Q79. t½=7h. Fraction after 14h:

Difficulty: Easy-Medium · Topic: Decay

Solution

2 half-lives. (1/2)^2=1/4.

Q80. t½=7h. Fraction after 21h:

Difficulty: Easy-Medium · Topic: Decay

Solution

3 half-lives. (1/2)^3=1/8.

Q81. t½=7h. Fraction after 28h:

Difficulty: Easy-Medium · Topic: Decay

Solution

4 half-lives. (1/2)^4=1/16.

Q82. t½=7h. Fraction after 35h:

Difficulty: Easy-Medium · Topic: Decay

Solution

5 half-lives. (1/2)^5=1/32.

Q83. t½=7h. Fraction after 42h:

Difficulty: Easy-Medium · Topic: Decay

Solution

6 half-lives. (1/2)^6=1/64.

Q84. t½=7h. Fraction after 49h:

Difficulty: Easy-Medium · Topic: Decay

Solution

7 half-lives. (1/2)^7=1/128.

Q85. t½=8h. Fraction after 8h:

Difficulty: Easy-Medium · Topic: Decay

Solution

1 half-lives. (1/2)^1=1/2.

Q86. t½=8h. Fraction after 16h:

Difficulty: Easy-Medium · Topic: Decay

Solution

2 half-lives. (1/2)^2=1/4.

Q87. t½=8h. Fraction after 24h:

Difficulty: Easy-Medium · Topic: Decay

Solution

3 half-lives. (1/2)^3=1/8.

Q88. t½=8h. Fraction after 32h:

Difficulty: Easy-Medium · Topic: Decay

Solution

4 half-lives. (1/2)^4=1/16.

Q89. t½=8h. Fraction after 40h:

Difficulty: Easy-Medium · Topic: Decay

Solution

5 half-lives. (1/2)^5=1/32.

Q90. t½=8h. Fraction after 48h:

Difficulty: Easy-Medium · Topic: Decay

Solution

6 half-lives. (1/2)^6=1/64.

Q91. t½=8h. Fraction after 56h:

Difficulty: Easy-Medium · Topic: Decay

Solution

7 half-lives. (1/2)^7=1/128.

Q92. t½=9h. Fraction after 9h:

Difficulty: Easy-Medium · Topic: Decay

Solution

1 half-lives. (1/2)^1=1/2.

Q93. t½=9h. Fraction after 18h:

Difficulty: Easy-Medium · Topic: Decay

Solution

2 half-lives. (1/2)^2=1/4.

Q94. t½=9h. Fraction after 27h:

Difficulty: Easy-Medium · Topic: Decay

Solution

3 half-lives. (1/2)^3=1/8.

Q95. t½=9h. Fraction after 36h:

Difficulty: Easy-Medium · Topic: Decay

Solution

4 half-lives. (1/2)^4=1/16.

Q96. t½=9h. Fraction after 45h:

Difficulty: Easy-Medium · Topic: Decay

Solution

5 half-lives. (1/2)^5=1/32.

Q97. t½=9h. Fraction after 54h:

Difficulty: Easy-Medium · Topic: Decay

Solution

6 half-lives. (1/2)^6=1/64.

Q98. t½=9h. Fraction after 63h:

Difficulty: Easy-Medium · Topic: Decay

Solution

7 half-lives. (1/2)^7=1/128.

Q99. t½=10h. Fraction after 10h:

Difficulty: Easy-Medium · Topic: Decay

Solution

1 half-lives. (1/2)^1=1/2.

Q100. t½=10h. Fraction after 20h:

Difficulty: Easy-Medium · Topic: Decay

Solution

2 half-lives. (1/2)^2=1/4.

Q101. t½=10h. Fraction after 30h:

Difficulty: Easy-Medium · Topic: Decay

Solution

3 half-lives. (1/2)^3=1/8.

Q102. t½=10h. Fraction after 40h:

Difficulty: Easy-Medium · Topic: Decay

Solution

4 half-lives. (1/2)^4=1/16.

Q103. t½=10h. Fraction after 50h:

Difficulty: Easy-Medium · Topic: Decay

Solution

5 half-lives. (1/2)^5=1/32.

Q104. t½=10h. Fraction after 60h:

Difficulty: Easy-Medium · Topic: Decay

Solution

6 half-lives. (1/2)^6=1/64.

Q105. t½=10h. Fraction after 70h:

Difficulty: Easy-Medium · Topic: Decay

Solution

7 half-lives. (1/2)^7=1/128.

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 12: AtomsCh 14: Semiconductor Electronics

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