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.)

To determine the half-life of a radioactive element, a student plots a graph of $$\ln \left| {{{dN(t)} \over {dt}}} \right|$$ versus t. Here, $${{dN(t)} \over {dt}}$$ is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is __________.