A Radioactive Problem

Chemistry Level 4

Plutonium-239 has been used as a power source for heart pacemakers. The chemical reaction taking place is

\[_{94}^{239}\ce{Pu} \longrightarrow _{2}^{4}\ce{He} + _{92}^{235}\ce{U}\]

Let the energy obtained from the following decay of \(215 \ \text{mg}\) of plutonium-239 be \(A \ \text{J}\).

Let \(B \ \text{g}\) be the minimum mass of \(\text{Zn}\) that would be needed for the standard voltaic cell

\[\ce{Zn} \ | \ \ce{Zn^{2+}} \ || \ \ce{Cu^{2+}} \ | \ \ce{Cu}\]

to obtain the same amount of electrical energy.

What is the value of \(\frac{A}{1000B}\) when rounded to the nearest integer?

Details and Assumptions

  • Standard cell potential: \(E^{\circ}_{\text{cell}} = 1.1 \ \text{V}\).
  • Atomic masses: \(\ce{He} = 4.0015 \ \text{u}, \ce{U} = 234.9935 \ \text{u}, \ce{Pu} = 239.0006 \ \text{u}\).

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