Problem

Polonium (

^{210}_{84}\text{Po}

) emits

^4_2\text{He}

particles and is converted into lead (

^{206}_{82}\text{Pb}

). This reaction is used for producing electric power in a space mission.

^{210}\text{Po}

has half-life of 138.6 days. Assuming an efficiency of 10% for the thermoelectric machine, how much

^{210}\text{Po}

is required to produce

1.2 \times 10^7

J of electric energy per day at the end of 693 days? Also find the initial activity of the material. Masses of nuclei:

^{210}\text{Po} = 209.98264 \text{ amu}, \quad ^{206}\text{Pb} = 205.97440 \text{ amu}, \quad ^4_2\text{He} = 4.00260 \text{ amu},

1 \text{ amu} = 931 \text{ MeV}/c^2 \text{ and Avogadro's number} = 6 \times 10^{23}/\text{mol}