Polonium emits particles and is converted into lead

PHYSICS · Subjective · CBSE · Physics · Nuclei · Nuclei

Problem

Polonium

\left({}^{210}_{84}\text{Po}\right)

emits

{}^{4}_{2}\text{He}

particles and is converted into lead

\left({}^{206}_{82}\text{Pb}\right)

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

{}^{210}\text{Po}

has a 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\times10^7\,\text{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\quad\text{and}\quad N_A=6\times10^{23}\,\text{mol}^{-1}.