A small laboratory heater requires a steady power of

PHYSICS · Multi-part · CBSE · Physics · Nuclei · Nuclei

Problem

1.0\,\text{kW}

. The heater is to be run by completely fissioning a

2.0\,\text{g}

capsule of enriched

^{235}\text{U}

, each fission event releasing

200\,\text{MeV}

of energy. Take

N_A = 6.022\times10^{23}\,\text{mol}^{-1}

and

1\,\text{eV} = 1.6\times10^{-19}\,\text{J}

. (i) Calculate the total energy, in joule, liberated when all the nuclei in the

2.0\,\text{g}

sample undergo fission. (ii) Only

25\%

of the liberated energy is converted into useful heat for the heater. For how many days can the heater deliver

1.0\,\text{kW}

continuously with this efficiency?