Nuclei

34 solved questions from Class 12 Physics, each with the full working. Tap any question to see the step-by-step solution.

• 1 What is the fundamental law or governing principle of 'Nuclei' in Class 12 Physics? medium MCQ Fundamental Physical Law
• 2 What is the SI unit and dimensional formula for the key physical quantity studied in 'Nuclei'? medium MCQ SI Units & Dimensional Analysis
• 3 How does the field or potential intensity vary with distance r in 'Nuclei'? medium MCQ Spatial Distance Dependence
• 4 What is the net flux or circulation integral through a closed surface in 'Nuclei'? medium MCQ Gauss's Theorem & Boundary Integrals
• 5 Why do field lines in 'Nuclei' never intersect each other? medium MCQ Field Line Properties
• 6 A sample of a radioactive isotope contains N_0=1.0×10^6 nuclei. After 15 days only 2.5×10^5 nuclei remain. What is the half‑life of the isotope? (Assume exponential decay). medium MCQ 3 marks Half‑life calculation using decay law
• 7 The fission of a ^235U nucleus after capturing a thermal neutron can be represented as ^235U + ^1n → ^141Ba + ^92Kr + 3 ^1n. Given the atomic masses: m(^235U) = 235.0439 u, m(^1n) = 1.008665 u, m(^141Ba) = 140.9144 u, m(^92Kr) = 91.9262 u. Calculate the total energy released in this fission reaction. (1 u = 931.5 MeV/c^2). hard 5 marks Energy released in nuclear fission (mass‑energy equivalence)
• 8 Explain why, for the same kinetic energy, alpha particles travel a shorter distance in air than beta particles. medium 2 marks Range of charged particles in matter
• 9 The atomic mass of a helium‑4 nucleus is 4.002603 u, the mass of a proton is 1.007276 u and the mass of a neutron is 1.008665 u. Calculate the binding energy per nucleon of the helium‑4 nucleus. (1 u = 931.5 MeV/c^2). easy 3 marks Binding energy per nucleon
• 10 In β^- decay, which of the following particles is emitted from the nucleus? easy MCQ 1 mark Particle emitted in beta‑minus decay
• 11 The fusion reaction D + T → ^{4}He + n releases energy. Given atomic masses: m(^{2}H)=2.014102 u, m(^{3}H)=3.016049 u, m(^{4}He)=4.002603 u, m(n)=1.008665 u. (1 u = 931.5 MeV/c^2). (a) Calculate the total energy released per reaction. (b) If 1 g of deuterium (pure D_2 gas) reacts completely with tritium in stoichiometric proportion, find the total energy released in joules. hard 5 marks Energy from nuclear fusion reaction
• 12 An initially prepared sample contains 5.0×10^5 atoms of a radioactive isotope. After 24 days only 6.25×10^4 atoms remain. Determine the half‑life of the isotope. medium 3 marks Half‑life from decay data
• 13 Given: mass of a deuteron (^{2}H) = 2.014102 u, mass of a proton = 1.007276 u, mass of a neutron = 1.008665 u. Compute the binding energy per nucleon of the deuteron nucleus. (1 u = 931.5 MeV/c^2). easy 2 marks Binding energy per nucleon
• 14 A sample initially contains 2.0×10^4 nuclei of a radioactive isotope whose half‑life is 8 days. How many nuclei remain after 24 days? medium 3 marks Radioactive decay law
• 15 The mass of a ^3He nucleus is 3.016029 u, the mass of a proton is 1.007276 u and the mass of a neutron is 1.008665 u. Using 1 u=931.5 MeV/c^2, calculate the binding energy per nucleon of the ^3He nucleus. easy 2 marks Binding energy per nucleon
• 16 Consider the fission of ^235U induced by a thermal neutron: ^235U+^1n→^92Kr+^141Ba+3 ^1n Atomic masses (in u): m(^235U)=235.0439, m(^1n)=1.008665, m(^92Kr)=91.9262, m(^141Ba)=140.9144. hard 5 marks Energy released in nuclear fission and power calculations
• 17 A sample contains 1.5×10^5 nuclei of a radioactive isotope whose half‑life is 6 days. How many nuclei remain after 18 days? medium 4 marks Radioactive decay calculation
• 18 In the fusion reaction ^3H+^3He→^6Li+γ, the atomic masses are: m(^3H)=3.016049 u, m(^3He)=3.016029 u, m(^6Li)=6.015122 u, and photon mass is zero. (a) Calculate the energy released per reaction in MeV. (b) If 0.5 g of tritium reacts completely with 0.5 g of helium‑3, find the total energy released in joules. hard 5 marks Fusion reaction energy calculation
• 19 What is the binding energy per nucleon of a −42×Ν nucleus if its mass is −42.000000 u, the mass of a proton is −41.007276 u and the mass of a neutron is −41.008665 u? easy MCQ 3 marks Binding energy per nucleon
• 20 Calculate the binding energy per nucleon of the ^56Fe nucleus. The nuclear mass is 55.934937 u, mass of a proton 1.007276 u, mass of a neutron 1.008665 u. Use 1,u=931.5,MeV/c^2. hard 3 marks binding energy per nucleon, mass defect
• 21 For the alpha decay ^241Am→^237Np+α, the masses are m(^241Am)=241.05682 u, m(^237Np)=237.04817 u, m(α)=4.002603 u. Calculate the Q‑value of the reaction. easy 2 marks Q‑value of nuclear decay
• 22 A sample contains 3.0×10^5 atoms of a radioactive isotope. After 12 days only 6.0×10^4 atoms remain. Find the half‑life of the isotope. medium 2 marks exponential decay, half‑life
• 23 The fusion reaction ^2H+^3He→^4He+p has the following atomic masses: m(^2H)=2.014102 u, m(^3He)=3.016029 u, m(^4He)=4.002603 u, m(p)=1.007276 u. (a) Calculate the energy released per reaction (Q‑value) in MeV. (b) If 2.0 g of deuterium reacts completely with excess ^3He, find the total energy released in joules. (Take 1 u=931.5 MeV/c^2 and 1 MeV=1.602×10^-13 J.) hard 5 marks Fusion Q‑value and total energy calculation
• 24 The beta‑minus decay ^60Co→^60Ni+e^-+u_e occurs with the following atomic masses: m(^60Co)=59.933822 u, m(^60Ni)=59.930786 u, and the electron mass m_e=0.00054858 u. (a) Calculate the Q‑value of the decay in MeV. (b) Assuming the neutrino carries negligible kinetic energy, find the maximum kinetic energy of the emitted electron (in MeV). hard 4 marks Q‑value of $\beta^{-}$ decay
• 25 An initial sample contains 4.0×10^6 nuclei of a radioactive isotope. After 10 days only 1.0×10^6 nuclei remain. Assuming exponential decay, calculate the half‑life of the isotope (in days). medium 2 marks Radioactive decay law
• 26 The atomic mass of a deuteron (^2H) is 2.014102 u. The masses of a proton and a neutron are 1.007276 u and 1.008665 u respectively. Using 1 u=931.5 MeV/c^2, calculate the binding energy per nucleon of the deuteron nucleus. easy 1 mark Binding energy per nucleon
• 27 A radioactive isotope has an initial activity of 4.0×10^6 nuclei. After 10 days only 1.0×10^6 nuclei remain.\n(a) Assuming exponential decay, determine the half‑life T_(1/2) of the isotope (in days).\n(b) Using the half‑life found in part (a), calculate how many nuclei will be left after 30 days. hard 4 marks Exponential decay and half‑life
• 28 Consider the fission of ^235U induced by a thermal neutron: ^235U+^1n→^92Kr+^141Ba+3 ^1n Atomic masses (in u) are: m(^235U)=235.0439, m(^1n)=1.008665, m(^92Kr)=91.9262, m(^141Ba)=140.9144.\n(a) Calculate the Q‑value (energy released) per fission reaction in MeV.\n(b) If 0.5 g of ^235U undergoes complete fission, find the total energy released in joules. (Use 1 u=931.5 MeV and 1 MeV=1.602×10^-13 J.)\n(c) How many fissions per second are required to produce a thermal power of 500 MW? hard 5 marks Energy release in nuclear fission
• 29 A sample contains 5.0×10^5 nuclei of a radioactive isotope. After 12 days only 6.0×10^4 nuclei remain. Assuming exponential decay, find the half‑life of the isotope (in days). medium 3 marks Half‑life calculation
• 30 Calculate the binding energy per nucleon of the ^4He nucleus. The atomic mass of ^4He is 4.002603,u. The masses of a proton and a neutron are 1.007276,u and 1.008665,u respectively. Use 1,u=931.5,MeV/c^2. easy 2 marks Binding energy per nucleon
• 31 Consider the fission of ^235U induced by a thermal neutron: ^235U+^1n→^92Kr+^141Ba+3,^1n Atomic masses (in u) are: m(^235U)=235.0439, m(^1n)=1.008665, m(^92Kr)=91.9262, m(^141Ba)=140.9144. hard 5 marks Fission energy and power conversion
• 32 Which of the following particles is emitted from the nucleus during a β^- decay? easy MCQ 1 mark Beta decay emission
• 33 The alpha decay of polonium‑210 is given by ^210Po→^206Pb+alpha. The atomic masses are m(^210Po)=209.98785 u, m(^206Pb)=205.9725 u, and m(α)=4.002603 u. Using 1 u=931.5 MeV/c^2, calculate the Q‑value of the decay. Assume the neutrino carries negligible kinetic energy. medium 3 marks $Q$‑value of alpha decay
• 34 A sample contains 5.0×10^5 nuclei of a radioactive isotope. After 24 days, only 6.25×10^4 nuclei remain. Which of the following is the half‑life of the isotope? easy MCQ 2 marks Half‑life from exponential decay