By considering the three-dimensional harmonic oscillator potential, explain the energy levels of nucleons inside the nucleus. Also, derive the zero-point energy of nucleons. Why did this assumption fail to explain the existence of nuclei with higher magic number?
A nucleus of rest mass M is initially in an excited state whose energy is \Delta E above its ground state. The nucleus emits a \gamma-ray of energy h\nu and makes a transition to its ground state. Calculate the fractional change in energy for the nucleus.
What is the criticality of a self-sustained nuclear reactor? Write the basic processes affecting the nuclear chain reactions of a finite-size nuclear reactor. Also, write the critical size of reactors of different shapes in terms of geometrical buckling constant.
Are the nucleons inside the nucleus governed by the laws of quantum physics? Justify your answer.
What do you understand by the \text{SU}(3) symmetry for the classification of baryons and mesons? Draw the octets for baryons and mesons along with their quarks and antiquarks.
What do you understand by the packing fraction 'f' and the binding energy 'E_b' of a nucleus? Draw the graphs for packing fraction f versus mass number (A) and binding energy fraction f_b \left(= \dfrac{E_b}{A}\right) versus mass number (A). Further, explain how the graphs of the variation of f and f_b with A have complementary approaches.
Binding energy and rest mass energy of a two-nucleon bound state are denoted by B and Mc^2, respectively, where c is the speed of light. Calculate the minimum energy of a photon required to dissociate this bound state in terms of B and Mc^2.
The total binding energies of {}_8^{15}\text{O}, {}_8^{16}\text{O} and {}_8^{17}\text{O} are 111\cdot 96 \text{ MeV}, 127\cdot 62 \text{ MeV} and 131\cdot 76 \text{ MeV} respectively. Determine the energy gap between 1p_{1/2} and 1d_{5/2} neutron shells for the nuclide whose mass number is close to 16.
State the basic assumption of single-particle shell model. How do the centrifugal and spin-orbit terms remove the degeneracy of three-dimensional spherical harmonic oscillator?
\rho^0 and \text{K}^0 mesons both decay mostly to \pi^+ and \pi^-. Why the mean lifetime of \rho^0 is 10^{-23} \text{ s}, whereas that of \text{K}^0 is 0\cdot 89 \times 10^{-10} \text{ s}?
(i) \pi^- \rightarrow \mu^- + \bar{\nu}_\tau (ii) n \rightarrow p^+ + e^- + \bar{\nu}_e Explain the various leptonic family members. What is leptonic number conservation? Based on this conservation law, tell whether the following reactions are possible or not : (i) \pi^- \rightarrow \mu^- + \bar{\nu}_\tau (ii) n \rightarrow p^+ + e^- + \bar{\nu}_e
Consider a uranium nucleus ({}_{92}\text{U}^{236}) breaking up spontaneously into two equal parts. Estimate the reduction of electrostatic energy of the nucleus considering uniform charge distribution. [ Assume that nuclear radius is 1\cdot 2 \times 10^{-13} A^{1/3} \text{ cm} ]
What is the minimum energy required to break a {}_2^4\text{He} nucleus into free protons and neutrons? [ Given, m_{\text{H}} = 1\cdot 007825 \text{ amu}, m_n = 1\cdot 008665 \text{ amu}, m_e = 0\cdot 00055 \text{ amu} and m_{\text{He}} = 4\cdot 002603 \text{ amu} ]
(i) Write semi-empirical mass formula. Calculate the atomic number (Z) of most stable nucleus for given mass number (A) using the above formula. (Use the value of fitted coefficients for Coulomb energy a_3 = 0\cdot 711\text{ MeV} and that for asymmetry energy a_4 = 23\cdot 702\text{ MeV}). (ii) Calculate the Q-value of the following nuclear reaction : {}_4\text{Be}^9 + {}_2\text{He}^4 = {}_6\text{C}^{12} + {}_0\text{n}^1 Given : the mass of neutral atoms of \text{Be}, \text{He} and \text{C} are 9\cdot 015060, 4\cdot 003874 and 12\cdot 003815\text{ amu}, respectively. The mass of neutron is 1\cdot 008986\text{ amu}.
Does the nucleus possess magnetic moment ? Justify your answer. Define nuclear magneton (\mu_{\text{N}}) and Bohr magneton (\mu_{\text{B}}). Calculate their values.
What is nuclear resonance absorption of gamma rays ? Describe the working and applications of Mossbauer spectrometer.
Compare nuclear density of hydrogen ({}_1\text{H}^1) with its atomic density. (Assume the atom to have the radius of its first Bohr orbit). What inference can one get from the above comparison ?
For the ground state of deuteron, prove that the radius of nucleon is of the order of \sim 2\cdot 15 \times 10^{-13}\text{ cm}.
(ii) \bar{\nu}_e + p^+ \rightarrow n^0 + e^- What are the various conservation laws for elementary particles ? Apply these conservation laws to confirm whether the following reactions are possible or not : (i) \pi^+ + n^0 \rightarrow K^0 + K^+ (ii) \bar{\nu}_e + p^+ \rightarrow n^0 + e^-
What is meant by strength of the interactions of elementary particles ? Classify the different forces on the basis of this strength of interaction.
