Mean lifetime τ of radioactive nucleus vs half-life T₁/₂:
Aτ = 2 × T₁/₂
Bτ = T₁/₂ × ln 2
Cτ = T₁/₂
Dτ = T₁/₂ / ln 2 ≈ 1.44 × T₁/₂
Answer & Solution
Correct answer: D. τ = T₁/₂ / ln 2 ≈ 1.44 × T₁/₂
τ = 1/λ = T₁/₂ / ln 2 ≈ 1.443 × T₁/₂. Mean lifetime ≈ 1.44 × half-life. After τ, N drops to N₀/e ≈ 37%.
Related questions
For He⁺ ion (Z = 2), energy of n=1 (ground state):In a hydrogen atom transition from n=4 to n=2, the emitted photon belongs to:Activity of 1 gram of ²²⁶Ra (Avogadro = 6 × 10²³; T₁/₂ = 1600 yr):Mass-energy equivalence: rest energy of electron (m_e = 9.11 × 10⁻³¹ kg):For ¹H ground state to first excited state (n=2), photon required:Nuclear radius R relates to mass number A as:Wavelength of de Broglie wave of electron in n-th Bohr orbit:Energy released in fusion: 4 protons → He-4 + 2 e⁺ + 2 ν_e (solar fusion). About: