A radioactive metal sphere of diameter 3.2 × 10⁻³ m emits β⁻-particles at a constant rate 6.25 × 10¹⁰ s⁻¹. The sphere is electrically insulated and the β⁻-particles leave from its surface. How long will it take for the sphere potential to rise to 1 V?
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Question

A radioactive metal sphere of diameter 3.2 × 10⁻³ m emits β⁻-particles at a constant rate 6.25 × 10¹⁰ s⁻¹. The sphere is electrically insulated and the β⁻-particles leave from its surface. How long will it take for the sphere potential to rise to 1 V?

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G1 Physics · Accepted Answer

Step 1: Use N(t) = N₀ exp(−λt), A = λN and T₁/₂ = ln2/λ. Step 2: For two samples, write the decay law separately and equate the required activities/numbers. Final: C: 18 μs.