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question_answer1) Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At \[t\text{ }=\text{ }0\] it was 1600 counts per second and t \[=\text{ }8\] seconds it was 100 counts per second. The count rate observed, as counts per second, at \[t\text{ }=\text{ }6\] seconds is
question_answer2) The ratio of the mass densities of nuclei of \[^{40}Ca\] and \[^{16}O\] is
question_answer3) The activity of a freshly prepared radioactive sample is \[{{10}^{10}}\] disintegrations per second, whose mean life is \[{{10}^{9}}\] s. The mass of an atom of this radioisotope is \[{{10}^{-25}}kg.\] The mass (in mg) of the radioactive sample is
question_answer4) A radioactive element decays by \[\beta \] emission. A detector records n beta particles in 2 second and in next 2 seconds it records 0.75 n beta particles. Find mean life (in second) corrected to nearest whole number. Given \[\ln 2=0.6931\] and \[\ell n3=\text{ }1.0986.\]
question_answer5) The half-life of radon is 3.8 days. After how many days will only one twentieth of radon sample be left over?
question_answer6) The count rate from a radioactive sample falls from \[4.0\times {{10}^{6}}\] per second to \[1\times {{10}^{6}}\] per second in 20 hour. What will be the count rate per second 100 hour after the beginning?
question_answer7) In an ore containing uranium, the ratio of \[{{U}^{238}}\]to \[P{{b}^{206}}\]nuclei is 3. Calculate the age of the ore, (in year) assuming that all the lead present in the ore in the final stable product of \[{{U}^{238}}\]. Take the half-life of \[{{U}^{238}}\]to be \[4.5\times {{10}^{9}}\] year.
question_answer8) In a nuclear reactor \[{{U}^{235}}\] undergoes fission liberating 200 MeV of energy. The reactor has 10% efficiency and produces 1000 MW power. If the reactor is to function for 10 year, find the total mass (in kg) of the uranium required.
question_answer9) A radioactive source, in the form of a metallic sphere of radius \[{{10}^{-2}}m\] emits (\[\beta \] - particles at the rate of \[5\times {{10}^{10}}\] particles per second. The source is electrically insulated. How long (in second) will it take for its potential to be raised by 2V, assuming that 40% of the emitted \[\beta \]- particles escapes the sources?
question_answer10) It is proposed to use the nuclear fusion reaction \[_{1}{{H}^{2}}{{+}_{1}}{{H}^{2}}\to 2H{{e}^{4}}\] in a nuclear reactor of 200 MW rating. If the energy from the above reaction is used with 25% efficiency in the reactor, how many gram of deuterium fuel will be needed per day? (The masses of \[_{1}{{H}^{2}}\] and \[_{2}H{{e}^{4}}\] are 2.0141 amu and 4.0026 amu respectively).
question_answer11) \[{{A}^{7}}\text{ }Li\] target is bombarded with a proton beam current of \[{{10}^{-4}}\] A for 1 hour to produce \[^{7}Be\] of activity \[1.8\times {{10}^{8}}\] disintegrations per second. Assuming that one \[^{7}Be\] radioactive nucleus is produced by bombarding 1000 protons, determine its half-life (in second)
question_answer12) The disintegration rate of a certain radioactive sample at any instant is 4750 disintegrations per minute. Five minutes later the rate becomes 2700 disintegrations per minute. Calculate half-life of the sample (in minute)
question_answer13) If the radius of a nucleus \[^{256}X\] is 8 fermi, then the radius (in fermi) of \[^{4}He\] nucleus will be
question_answer14) The mass defect for the nucleus of helium is 0.0303 a.m.u. What is the binding energy per nucleon for helium in MeV?
question_answer15) The radius of germanium (Ge) nuclide is measured to be twice the radius of \[_{4}^{9}Be\]. The number of nucleons in Ge are
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