Nuclei

Step 1: Best fuel should be fissile.
Step 2: ²³⁹Pu undergoes fission with thermal neutrons.

Step 1: Mass-energy conversion. A small fraction (~0.1%) of mass converts into energy during fission.
Step 2: Eliminating wrong options. Energy released is ~200 MeV, not eV, and more than one neutron is released.

Step 1: Binding energy per nucleon.
The stability of a nucleus is generally given by its binding energy per nucleon. The nucleus with the highest binding energy per nucleon is the most stable. The binding energy per nucleon for is the highest among the options, making it the most stable nucleus.
Thus, the correct answer is (1).

Step 1: By conservation of momentum, both nuclei have equal momentum.
Step 2: Kinetic energy:
Step 3: Smaller mass (helium) has larger kinetic energy.

Step 1: Mass defect: Δ m = m(¹5N) + mp - m(¹6O)
Step 2: Δ m = 15.00011 + 1.00783 - 15.99492 = 0.01302amu
Step 3: Binding energy: E = Δ m × 931 ≈ 2.13MeV

Step 1: Let initial atoms be N₀.
Step 2: Given ratio: (NX)/(NY) = (1)/(4) ⟹ NX = (N₀)/(5)
Step 3: Radioactive decay law: (NX)/(N₀) = ((1)/(2))ᵗ/2 = (1)/(5) ⟹ t ≈ 4.6h

Step 1: Mass converted Δ m = 0.1% × 1 = 10⁻3 kg
Step 2: Energy released E = Δ m c² = 10⁻3 × (3 × 10⁸)² = 9 × 10¹3 J

Step 1: (1)/(16) = ((1)/(2))⁴
Step 2: Four half-lives occur in 2 hours.
Step 3: T₁/2 = (120)/(4) = 30 minutes

Step 1: Number of nuclei at time t: N=(R)/(λ)(1-e⁻λ t)
Step 2: 25=(50)/(0.5)(1-e⁻0.5t) ⟹ 1-e⁻0.5t=(1)/(4)
Step 3: e⁻0.5t=(3)/(4) ⟹ t=2ln((4)/(3))

Step 1: Total binding energies: B₁0 = 10 × 9 = 90MeV B₁1 = 11 × 7.5 = 82.5MeV
Step 2: Energy required: E = B₁0 - B₁1 + neutron energy
Step 3: E = 2.5MeV

Step 1: Let initial number of uranium nuclei be N₀. Present uranium nuclei N = 3, lead nuclei =1. (N)/(N₀ - N) = 3 ⟹ N₀ = 4
Step 2: Radioactive decay law: (N)/(N₀) = ((1)/(2))ᵗ/T_¹/² (3)/(4) = ((1)/(2))ᵗ/⁴.⁵ᵗⁱᵐᵉˢ¹⁰^⁹
Step 3: Solving, t = 1.867 × 10⁹yr

Step 1: Proton separation energy: Sp = [M(ce¹5N) + mp - M(ce¹6O)]c²
Step 2: Substituting atomic masses (electrons cancel): Δ m = 15.00011 + 1.00783 - 15.99492 = 0.01302u
Step 3: Converting mass defect to energy: Sp = 0.01302 × 931 ≈ 12.13MeV

Step 1: Let the initial number of atoms be N₀. After time t: NX = (N₀)/(5), NY = (4N₀)/(5)
Step 2: Radioactive decay law: NX = N₀((1)/(2))ᵗ/T_¹/²
Step 3: Substituting values: (1)/(5) = ((1)/(2))ᵗ/2
Step 4: Taking logarithm: (t)/(2) = log₂ 5 ≈ 2.32 ⟹ t ≈ 4.64h Closest option is 4h.

Step 1: Understanding the Concept
In a nuclear fusion reaction, energy is released when the total binding energy of the product nucleus is greater than the total binding energy of the reactant nuclei. The energy released ( -value) is the difference between these two.

Step 2: Key Formula or Approach
1. Total Binding Energy (B.E.) = (B.E. per nucleon) (Number of nucleons, ) 2. Energy released = (Total B.E. of products) (Total B.E. of reactants)

Step 3: Detailed Explanation
1. Reactants ( nuclei of ): - Each nucleus has . - B.E. per nucleon = 1.1 MeV. - Total B.E. of reactants = MeV. 2. Product ( nucleus of ): - Nucleus has . - B.E. per nucleon = 7.6 MeV. - Total B.E. of product = MeV. 3. Energy Released: - MeV.

Step 4: Final Answer
The energy released in the process is 26 MeV.