Modern Physics-07-PROBLEMS

PROBLEMS 1. The element curium Cm has a mean life of seconds. Its primary decay modes are spontaneous fission and decay, the former with a probability of 8% and the latter with a probability of 92%. Each fission release 200 MeV of energy. The masses involved in decay are as follows : Calculate the power output form a sample of Cm atoms. (1u = 931meV/c2). 2. Nuclei of a radioactive element A are being produced at a constant rate . The element has decay constant . At time t = 0, there are N0 nuclei of the element. (a) Calculate the number N of nuclei of A at time t. (b) If , calculate the number of nuclei of A after one half life of A and also the limiting value of N as t . 3. (a) A hydrogen like atom of atomic number Z is in an excited state of quantum number 2n. It can emit a maximum energy photon of 204 eV. If it makes a transition to quantum state n, a photon of energy 40.8 eV is emitted. Find n, Z and the ground state energy (in eV) of this atom. Also calculate the minimum energy (in eV) that can be emitted by this atom during de-excitation. Ground state energy of hydrogen atom is -13.6 eV. (b) when a beam of 10.6 eV photons of intensity 2.0 W/m2 falls on a platinum surface of area and work function 5.6 eV, 0.53% of the incident photons eject photoelectrons. Find the number of photoelectrons emitted per second and their minimum and maximum energies (in eV). Take 1eV = J. 4. In a nuclear reactor 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. 5. A nucleus at rest undergoes a decay emitting an - particle of de-Broglie wavelength, m. If the mass of the daughter nucleus is 223.610 a.m.u. and that of the - particle is 4.002 a.m.u., determine the total kinetic energy in the final state. Hence, obtain the mass of the parent nucleus in a.m.u. (1 a.m.u. = 931.470 MeV/c2) 6. A radioactive nucleus X decays to a nucleus Y with a decay constant . Y further decays to a stable nucleus Z with a decay constant . Initially, there are only X nuclei and their number is . Set up the rate equations for the populations of X, Y and Z. The population of the Y nucleus as a function of time is given by . Find the time at which is maximum and determine the populations X and Z at that instant. 7. A hydrogen-like atom (described by the Bohr model) is observed to emit six wavelengths, originating from all possible transitions between a group of levels. These levels have energies between -0.85 eV and 0.544 eV (including both these values). (a) Find the atomic number of the atom. (b) Calculate the smallest wavelength emitted in these transitions. (Take hc = 1240 eV –nm, ground state energy of hydrogen atom = - 13.6 eV. 8. Characteristic X-rays of frequency Hz are produced when transitions from L shell to K shell take place in a certain target material. Use Moseley’s law to determine the atomic number of the target material. Given Rydberg constant . 9. A radioactive element decays by emission. A detector records n beta particles in 2 seconds and in next 2 seconds it records 0.75 n beta particles. Find mean life correct to nearest whole number. Given ln |2| = 0.6931, In |3| = 1.0986. 10. In a photoelectric experiment setup, photons of energy 5 eV falls on the cathode having work function 3 eV. (a) If the saturation current is = 4 for intensity , then plot a graph between anode potential and current. (b) Also draw a graph for intensity of incident radiation . 11. A rock is years old. The rock contains , which disintegrates to forth . Assume that there was no in the rock initially and it is the only stable product formed by the decay. Calculate the ratio of number of nuclei of to that of in the rock Half – life of is years. . 12. Wavelength belonging to Balmer series lying in the range of 450 nm to 750 nm were used to eject photoelectrons from a metal surface whose work function is 2.0 eV. Find (in eV) the maximum kinetic energy of the emitted photoelectrons. Take hc = 1242 eV nm.