A nuclear power plant supplying electrical power to a village uses a radioactive material of half life T years as the fuel.

The amount of fuel at the beginning is such that the total power requirement of the village is 12.5 % of the electrical power available from the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of nT years, then the value of n is

A freshly prepared sample of a radioisotope of half-life 1386 s has activity 10³ disintegrations per second. Given that ln2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s after preparation of the sample is __________.

A proton is fired from very far away towards a nucleus with charge Q = 120e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the proton at its start is ____________. (Take the proton mass, $${m_p} = (5 \times 3) \times {10^{ - 27}}$$ kg; $$h/e = 4.2 \times {10^{ - 15}}$$ J.s/C; $${1 \over {4\pi {\varepsilon _0}}} = 9 \times {10^9}$$ m/F; 1 fm = 10¹⁵ m.)