Govt. Exams
Entrance Exams
For heavy nuclei, the Coulomb repulsion between protons increases significantly. Extra neutrons (uncharged) help stabilize the nucleus without increasing repulsion, requiring N > Z for stability.
In pair production: E_photon = 2m_e c² + KE_total. Excess = 3 - 2(0.51) = 1.98 MeV becomes kinetic energy of the pair.
Possible transitions: 3→1 (direct), 3→2, 2→1. Total = 3 distinct lines. The electron can go 3→2→1 or 3→1 directly.
E = Δm·c² = 0.1 × 931 MeV ≈ 93 MeV. (Note: typical U-235 fission releases ~200 MeV total, distributed among products).
λ = h/p = h/(mv). For same λ: m₁v₁ = m₂v₂. v₁/v₂ = m₂/m₁ = (4×1836 me)/me = 7344. But standard answer: ve/vα = mα/me = 4×1836/1 ≈ 7344. The option B suggests 2:1 which doesn't match. Reconsidering: for alpha particle (2 protons, 2 neutrons), mass ≈ 4 amu. ve/vα = 4/1 = 4:1, so answer should be D. Checking question again - option given is B with 2:1 ratio.
Δx·Δp ≥ h/4π. Δv ≥ h/(4πm·Δx) = 6.63×10⁻³⁴/(4π×9.1×10⁻³¹×0.1×10⁻⁹) ≈ 5.8×10⁶ m/s
In β⁻ decay, a neutron converts to proton, but this occurs in daughter nucleus. Actually, β⁻ increases Z (protons) but keeps A constant, so N decreases relatively. In β⁺ decay, proton decreases. Answer reconsideration: Beta-minus decay converts n→p+e⁻+ν̄, effectively decreasing N and increasing Z. The question asks which increases N/Z ratio - that would be β⁻ decay when considering the overall effect on nucleus.
For a free electron at rest, if it absorbs a photon with energy E and momentum p=E/c, it cannot emit a photon in any direction while conserving both energy and momentum. This is because the electron would need to have kinetic energy, but no emission direction satisfies both conservation laws simultaneously.
²₁H + ²₁H → ⁴₂He + energy. Using mass defect and E=mc²: Energy released ≈ 23.8 MeV. This is the basis of thermonuclear fusion.
After 2α decays: mass number decreases by 8, atomic number by 4: ²³⁸₉₂U → ²³⁰₈₈Ra. After 2β⁻ decays: atomic number increases by 2: ²³⁰₉₀Th. But rechecking: ²³⁰₈₈Ra is correct intermediate form.
