Write down the nucleonic configuration of {}^{7}\mathrm{Li}, {}^{12}\mathrm{C}, {}^{17}\mathrm{O} and {}^{27}\mathrm{Al} in the ground state of the nuclear shell model and hence calculate the corresponding ground state angular momenta and parities. How do the observed ground state angular momenta and parities agree with those predicted on the basis of shell model?
Explain parity violation in \beta-decay. Describe how parity violation was experimentally detected in the decay of {}^{60}\mathrm{Co}. Mention any other decay process in which the parity violation has been demonstrated.
What do you understand by H-one (HI) interstellar clouds and their importance to understand the universe.
With proper selection rules, construct the energy level diagram and allowed transitions for ESR spectrum of hydrogen atom.
In a Raman spectrum of a linear triatomic molecule, the first three lines are 4.86, 8.14 and 11.36\ \mathrm{cm^{-1}}. Calculate the rotational constant, B and the moment of inertia of the molecule. (Given h = 6.626 \times 10^{-27}\ \mathrm{J\,s}, C = 3.0 \times 10^{10}\ \mathrm{cm/sec.})
Discuss the fine structure of sodium D line. Draw D_1 and D_2 lines due to the transitions between {}^2P and {}^2S levels.
How are electrons distributed in the various sub-shells for n=3? Give the quantum numbers for the electrons in the second shell.
The term symbol for atomic states are quoted as {}^3P_2 and {}^2D_{5/2}. What are the values of L, S and J?
Why are Raman active vibrations and infrared vibrations in \mathrm{CO_2} molecule complementary to each other?
In a series of experiments on the determination of the mass of a certain elementary particle, the results showed a variation of \pm 20\,m_e, where m_e is the electron mass. Estimate the lifetime of the particle.
Show that the velocity of electron in the first orbit of hydrogen atom is \left(\frac{1}{137}\right)C where C is the velocity of light. (Given electronic charge = 1.602 \times 10^{-1}\ \mathrm{C} Planck Constant 6.63 \times 10^{-34}\ \mathrm{J.s}, permittivity = 8.85 \times 10^{-1}\ \mathrm{C^2\ N^{-1}\ m^{-2}})
The normalized wave function for the electron in the ground state of the hydrogen atom is given by \psi(r)=\dfrac{1}{\sqrt{\pi a_0^3}}e^{-r/a_0}, where a_0 is the radius of the first Bohr orbit. Calculate the probability of finding the electron within a distance r_0 of the proton in the ground state.
(i) Consider a beam of particles incident on a one-dimensional step function potential with energy E > V_0 as shown in the above figure. Solve the Schrödinger equation and obtain expressions for the reflection and transmission coefficients.
(ii) What are the limits of the reflection coefficient for E \to V_0 and E \to \infty?
(iii) Discuss the cases 0 < E < V_0 and E < 0.
Using the definition \vec{L}=\vec{r}\times\vec{p} of the orbital angular momentum operator, evaluate [L_x,L_y].
A thermally insulated ideal gas is compressed quasi-statically from an initial state with volume V_0 and pressure P_0 to a final state of volume V_f and pressure P_f. Show that the work done on the gas in the process is given by W=\frac{C_V}{R}\left(P_fV_f-P_0V_0\right) where C_V and R having standard meanings.
The vapour pressure, in mm of Hg, of a substance in solid state is given by the relation \ln p=23.03-\dfrac{3754}{T}, where T is in Kelvin. The vapour pressure, in mm of Hg, of the substance in liquid state is given by the relation \ln p=19.49-\dfrac{3063}{T}. Calculate
(i) the coordinates of the triple point, and
(ii) the latent heat of vaporisation at the triple point. Take Gas constant R=8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}.
In Leh, temperature of ice on a cold winter night is measured as -20^\circ\mathrm{C}. Calculate the change in entropy when 1\ \mathrm{kg} of ice is converted into steam at 100^\circ\mathrm{C}. Given specific heat capacity of ice is 500\ \mathrm{cal\,kg^{-1}\,K^{-1}}, latent heat of ice is 3.36\times10^5\ \mathrm{J\,kg^{-1}}, latent heat of steam is 2.26\times10^6\ \mathrm{J\,kg^{-1}} and J=4.2\ \mathrm{J\,cal^{-1}}.
N particles obeying Classical Statistics are distributed among three states having energies \varepsilon_1 = 0, \varepsilon_2 = k_{\mathrm B}T and \varepsilon_3 = 2k_{\mathrm B}T, where k_{\mathrm B} is Boltzmann constant. If the total equilibrium energy of the system is 1000k_{\mathrm B}T, calculate the value of N.
The coefficient of viscosity of helium at 27^\circ\mathrm{C} is 2 \times 10^{-5}\ \mathrm{kg\,m^{-1}\,s^{-1}}. Calculate
(i) the average speed and
(ii) the diameter of a helium molecule, if it is assumed that the gas obeys Maxwell-Boltzmann distribution. Given Boltzmann constant k_{\mathrm B} = 1.38 \times 10^{-23}\ \mathrm{J\,K^{-1}} and mass of helium atom = 6.67 \times 10^{-27}\ \mathrm{kg}.
The electric field of a plane e.m. wave travelling along the z-axis is \vec{E}=(E_{0x}\hat{x}+E_{0y}\hat{y})\sin(\omega t-kz+\phi). Determine the magnetic field.
