(i) Distinguish between d.c. Josephson effect and a.c. Josephson effect. Show that Josephson effect exhibits the quantum interference phenomenon on macroscopic scale. (ii) The critical magnetic field of superconducting niobium is 1 \times 10^5\text{ A/m} at 8\text{ K} and 2 \times 10^5\text{ A/m} at 0\text{ K}. Calculate the critical transition temperature (T_c) of niobium.
An n-p-n transistor with \alpha = 0\cdot 98 is operated in the CB configuration. If the emitter current is 3\text{ mA} and the reverse saturation current is I_{CO} = 10\text{ }\mu\text{A}, what are the base current and the collector current?
(i) Prove the following using De Morgan's theorems : A \cdot B + C \cdot D = \overline{\overline{A \cdot B} \cdot \overline{C \cdot D}} (ii) Simplify the following expression : Y = A \cdot B \cdot \bar{C} \cdot D + \bar{A} \cdot B \cdot \bar{C} \cdot \bar{D} + B \cdot \bar{C} \cdot D
(i) Diamond and silicon have similar band structure. Why is diamond an insulator while silicon a semiconductor? (ii) An insulator has an optical absorption which occurs for all wavelengths lesser than 1400\text{ \AA}. Find the width of the forbidden energy band for the insulator.
What do you mean by strength of interaction among the elementary particles? Calculate the dimensionless coupling constants of gravitational and electromagnetic interactions.
Write the semi-empirical mass formula. Establish the relation A \approx 2Z, where A is mass number and Z is atomic number of the light nuclei, using this semi-empirical mass formula. [Given : good fitting coefficients for Coulomb energy (a_c) = 0\cdot 71\text{ MeV}, for asymmetry energy (a_n) = 22\cdot 7\text{ MeV}]
A reactor is developing nuclear energy at a rate of 3\cdot 2 \times 10^7\text{ watts}. How many atoms of \text{U}^{235} undergo fission per second? How many kg of \text{U}^{235} would be used up in 1000 hours of operation? Assume that an average energy of 200\text{ MeV} is released per fission. Take Avogadro number as 6 \times 10^{23} and 1\text{ MeV} = 1\cdot 6 \times 10^{-13}\text{ joule}.
(i) Show that pion decay, muon decay and pair production conserve lepton numbers L_e and L_\mu. (ii) Which of the following reactions is/are possible? Justify with reason : \bar{\nu}_e + p = n + \mu^+ \bar{\nu}_e + p \rightarrow n + e^+
(i) The radius of a nucleus is given to be 3\cdot 46\text{ fermi}. Estimate the mass number A of the nucleus and identify the nucleus. (ii) What is Bohr magneton? Find out the ratio of nuclear magnetic moment to Bohr magneton.
Explain how the nuclear shell model predicts the existence of magic numbers. Using shell model, predict the spin parity or characteristics of ground state of {}^{15}_8\text{O}, {}^{16}_8\text{O} and {}^{17}_8\text{O}.
(i) What is Q-value and how does it help to study the kinematics of a nuclear reaction? (ii) Prove that {}^{252}\text{Cf} can undergo spontaneous fission as under : {}^{252}\text{Cf} = {}^{98}\text{Zr} + {}^{145}\text{Ce} + 9 {}^{1}\text{n} Given : \begin{aligned} M(^{252}\text{Cf}) &= 252\cdot 081621\text{ a.m.u.}\\ M(^{98}\text{Zr}) &= 97\cdot 912735\text{ a.m.u.}\\ M(^{145}\text{Ce}) &= 144\cdot 917230\text{ a.m.u.}\\ M(^{1}\text{n}) &= 1\cdot 008665\text{ a.m.u.} \end{aligned}
The quantum numbers of the two optical electrons in a two-valence electron atom are n_1 = 6, \quad l_1 = 3, \quad s_1 = \frac{1}{2} n_2 = 5, \quad l_2 = 1, \quad s_2 = \frac{1}{2} Assuming j-j coupling, find the possible values of J.
Discuss the main features of the vibrational and the rotational Raman spectra of diatomic molecules. How is it used to explain the structure of a molecule?
The fine-structure lines of CN band at 3883\cdot 4\text{ \AA} can be represented by the following equation : \nu = 25798 + 3\cdot 85m + 0\cdot 068m^2\text{ cm}^{-1} Calculate the separation between the null-line and the band-head, and state the direction of degradation of the band.
Explain the mechanism of phosphorescence emission of radiation. Distinguish between fluorescence and phosphorescence.
Describe the basic principle of nuclear magnetic resonance (NMR) and mention its different applications.
Distinguish between normal and anomalous Zeeman effects. Explain the Zeeman pattern of the resonance (D_1, D_2) lines of sodium.
Find the values of the following : (i) \vec{L} \times \vec{L} (ii) L_+ L_- (iii) [L_z, L_+] where \vec{L} is the angular momentum operator. L_+ and L_- are raising and lowering operators respectively.
A one-dimensional oscillator of mass m = 10^{-20}\text{ kg} oscillates under a force constant k = 10^{-4}\text{ N/m}. (i) Evaluate the zero-point energy. (ii) Calculate the classical amplitude for which the oscillator can have this energy. (iii) What is the energy for the second excited state?
The lifetime of a given atom in an excited state is 10^{-8}\text{ s}. It comes to the ground state by emitting a photon of wavelength 5800\text{ \AA}. Find the energy uncertainty and wavelength uncertainty of the photon.
