Assuming that energy released by the fission of a single  \(_{ 92 }^{ 235 }{ U }\) nucleus is 200MeV, calculate the number of fissions per second required to produce 1-watt power.

Keezhadi ((கீழடி),a small hamlet, has become one of the very important archaeological places of Tamilnadu. It is located in Sivagangai district. A lot of artefacts (gold coins, pottery, beads, iron tools, jewellery and charcoal, etc.) have been unearthed in Keezhadi which have given substantial evidence that an ancient urban civilization had thrived on the banks of river Vaigai. To determine the age of those materials, the charcoal of 200 g sent for carbon dating is given in the following figure (b). The activity of \(_{ 6 }^{ 14 }{ C }\) is found to be 37 decays/s. Calculate the age of charcoal.

Figure (a) Keezhadi – excavation site

Figure (b) – Characol which was sent for carbon dating

Calculate the amount of energy released when 1 kg of \(_{ 92 }^{ 235 }{ U }\) undergoes fission reaction.

Explain the results of Rutherford α-particle scattering experiment.

Write the application of alpha decay in smoke detectors.

In a nuclear reactor, \(_{ }^{ 235 }U{ }\) undergoes fission liberating 200 MeV of energy. The reactor has a 10% efficiency and produces 1000 MW power. If the reactor is to function for 10 years, find the total mass of uranium required.

A radioactive nucleus X converts into stable nucleus Y. Half-life of X is 50 years. Calculate the age of the radioactive sample when the ratio of X and Y is 1:15.

Radon-222 is a radioactive gas for which the decay constant is 2.1 x 10^-6s^-1. If the initial decay rate is 5.6 x 10¹⁰s^-1, calculate:
(i) the initial number of radioactive atoms present and
(ii) the time which will elapse before the activity is reduced to one-quarter of Its initial value. Given: log_e 2 =0.693.

About 185 MeV of usable energy is released by the neutron-induced fissioning of a \(_{ 92 }^{ 235 }{ U }\) nucleus. If the reactor using \(_{ 92 }^{ 235 }{ U }\) as fuel continuously generates 100 MW of power, how long will it take for 1 kg of the uranium to be used up?

A piece of ancient wood shows an activity of 3.9 disintegrations per second per gram of ¹⁴C. Calculate the age of the wood. T_1/2 of ¹⁴C= 5568 years. Activity of fresh ¹⁴C= 15.6 disintegrations/s/gram.