Why does a neutron star have a magnetic field if it is composed of neutrons?

(i) K^+ \longrightarrow \Pi^+ + \Pi^+ + \Pi^- (ii) \Pi^+ + p \longrightarrow \Pi^+ + \Pi^+ + n (iii) \Pi^+ + p \longrightarrow \Delta^{++} \longrightarrow \Pi^+ + p (iv) \Sigma^\circ \longrightarrow \lambda^\circ + \gamma (v) \Sigma^+ \longrightarrow \lambda^\circ + e^+ + u_e (vi) K^- + p \longrightarrow K^+ + K^\circ + \Omega^- (vii) \Pi^\circ \longrightarrow \gamma + e^+ + e^- (viii) \Sigma^- \longrightarrow n + e^- + \bar{\nu}_e (ix) \lambda^\circ \longrightarrow p + e^- + \bar{\nu}_e (x) e^+ + e^- \longrightarrow \gamma + \gamma Name the interactions via which the above nuclear decays occur :

Often the intensity of rotational transition J = 0 \to J = 1 is not the most intense. Explain.

Evaluate the Land'e g-factor for the ^3\mathrm{P}_1 level in the 2p 3s configuration of the ^6\mathrm{C} atom, and then calculate the splitting of the level in eV, when the atom is in an external magnetic field of 0.2 tesla.

How does the Stern-Gerlach experiment explain the concept of electron spin and its angular momentum quantization?

(i) Homonuclear diatomic molecules do not give any pure rotational or vibrational spectra, whereas they do give a rotational Raman spectra. Comment. (ii) The separation between the adjacent rotational Raman lines is 4B in hydrogen molecule, whereas in oxygen molecule it is 8B. Why?

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What is Raman effect ? Explain Quantum theory of Raman effect and Rotational Structure of a Raman spectrum.

What is vector atom model ? How the principal features of vector atom model were explained by Stern-Gerlach experiment ?

What is Lande's g factor ? Evaluate the Lande's g factor for the {}^3P_1 level in the 2p3s configuration of the {}^6\text{C} atom. Also calculate the splitting of the level when the atom is placed in an external magnetic field of 0\cdot 1\text{ tesla}.

An atomic state is denoted by ^4\mathrm{D}_{5/2}. What should be the minimum number of electrons involved for this state? Give a possible electron configuration.

Discuss the influence of anharmonicity on the vibrational spectra of diatomic molecules with necessary diagrams.

If an atom is placed in a magnetic field of strength 0\cdot 1\text{ weber/m}^2, then calculate the rate of precession and torque on an electron with l=3 in the atom. Given that the magnetic moment of the electron makes an angle of 30^\circ with the magnetic field.

What is vector model of the atom? On the basis of it, explain the L-S and j-j coupling under external magnetic field.

What is nuclear magnetic resonance ? Explain its working principle and use in magnetic resonance imaging systems.

A beam of hydrogen atoms emitted from an oven at 400\text{ k} is sent through a Stern-Gerlach experiment having magnet of length 1\text{ m} and a gradient field of 10\text{ tesla/m}. Calculate the transverse deflection of an atom at the point where the beam leaves the magnet.

A particle constrained to move along x-axis in the domain 0 \le x \le L has a wave function \psi(x) = \sin \left( \frac{n \pi x}{L} \right), where n is an integer. Normalize the wave function and evaluate the expectation value of momentum of the particle.

The raising (J_+) and lowering (J_-) operators of total angular momentum are defined by J_+ = J_x + iJ_y and J_- = J_x - iJ_y. Find the values of the following : (i) [J_x, J_+] (ii) [J_y, J_+] (iii) J_- J_+

For the n^{\text{th}} state of linear harmonic oscillator, evaluate the uncertainty product (\Delta x) \cdot (\Delta p).

The components of arbitrary vectors \vec{A} and \vec{B} commute with those of \vec{\sigma}. Show that (\vec{\sigma} \cdot \vec{A})(\vec{\sigma} \cdot \vec{B}) = \vec{A} \cdot \vec{B} + i\vec{\sigma} \cdot (\vec{A} \times \vec{B}).