Half-life of radioactive sample is T₁/₂. Decay constant λ:
Aλ = 2 T₁/₂
Bλ = T₁/₂
Cλ = ln 2 / T₁/₂ ≈ 0.693/T₁/₂
Dλ = 1/T₁/₂
Answer & Solution
Correct answer: C. λ = ln 2 / T₁/₂ ≈ 0.693/T₁/₂
N(t) = N₀ e^(-λt). After T₁/₂, N = N₀/2 → e^(-λ T₁/₂) = 1/2 → λ T₁/₂ = ln 2 → λ = 0.693/T₁/₂.
Related questions
Mean lifetime τ of radioactive nucleus vs half-life T₁/₂: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: