Obtain the Q-values for the following four nuclear reactions :
(i) {}^{14}_{7}\text{N} + ^{4}_{2}\text{He} \rightarrow ^{17}_{8}\text{O} + ^{1}_{1}\text{H}
(ii) {}^{7}_{3}\text{Li} + ^{4}_{2}\text{He} \rightarrow ^{10}_{5}\text{B} + ^{1}_{0}\text{n}
(iii) {}^{6}_{3}\text{Li} + ^{1}_{1}\text{H} \rightarrow ^{3}_{2}\text{He} + ^{4}_{2}\text{He}
(iv) {}^{23}_{11}\text{Na} + ^{1}_{1}\text{H} \rightarrow ^{20}_{10}\text{Ne} + ^{4}_{2}\text{He}
What is Lamb shift? What is its significance in determining the fine structure of \mathrm{H}_{\alpha} Balmer line in hydrogen atom?
What is Raman effect? Describe briefly the chief characteristics of pure rotational spectra. The small rotational Raman displacement for HCl molecule is 41.6\ \mathrm{cm}^{-1}. Find the internuclear distance between the atoms forming the molecule.
Compute the allowed spectral terms for two non-equivalent p-electrons on the basis of Pauli’s exclusion principle.
In the Stern-Gerlach experiment using Ag atoms, the oven temperature is 1000 K, l \approx 25\ \mathrm{cm} and \frac{\partial B_z}{\partial z} \simeq 10^{+3}\,\text{Tesla/m}. Calculate the separation of the two components.
Describe Stern-Gerlach experiment. Discuss how it has explained space quantization and electron spin. Find the value of angle between the spin angular momentum \vec{S} and its z-component of an electron moving along the external magnetic field \vec{B}.
The series limit wavelength of Balmer series in hydrogen spectrum is experimentally found to be 3646\,\mathring{\mathrm{A}}. Find the wavelength of the first line of this series.
Explain in detail L-S coupling and j-j coupling schemes.
Consider a hydrogen atom in Bohr atomic model. Outline its importance in the context of spatial quantization and the spin of the electron.
Outline the Stern-Gerlach experiment and discuss its importance in the context of quantum nature of atom.
Obtain the frequency u_r of the spectral line of rotation spectra of a diatomic molecule and discuss the characteristics of its spectrum.
Outline elementary theory of Nuclear Magnetic Resonance (NMR) and discuss its applications.
Using uncertainty principle, calculate the size and energy of the ground state hydrogen atom.
Solve the Schrodinger equation for a step potential and calculate the transmission and reflection coefficient for the case when the kinetic energy of the particle E_0 is greater than the potential energy V (i.e., E_0>V).
A typical atomic radius is about 5 \times 10^{-15}\,m and the energy of \beta-particle emitted from a nucleus is at most of the order of 1\,\mathrm{MeV}. Prove on the basis of uncertainty principle that the electrons are not present in nuclei.
Write down the matrix representation of the three Pauli matrices \sigma_x, \sigma_y and \sigma_z. Prove that these matrices satisfy the following identities:
(i) [\sigma_x,\sigma_y]=2i\sigma_z
(ii) [\sigma^2\cdot\sigma_x]=0
(iii) (\vec{\sigma}\cdot\vec{A})(\vec{\sigma}\cdot\vec{B})=\vec{A}\cdot\vec{B}+i\vec{\sigma}\cdot(\vec{A}\times\vec{B}) if \vec{A} and \vec{B} commute with Pauli matrices.
Calculate the density of states for an electron moving freely inside a metal with the help of quantum mechanical Schrodinger's equation for free particle in a box.
An electron is confined to move between two rigid walls separated by 10^{-9}\,\mathrm{m}. Compute the de Broglie wavelengths representing the first three allowed energy states of the electron and the corresponding energies.
Find the energy, momentum and wavelength of photon emitted by a hydrogen atom making a direct transition from an excited state with n = 10 to the ground state. Also find the recoil speed of the hydrogen atom in this process.
Recall the Pauli matrix representation of two-state system of electron, \sigma_x, \sigma_y, \sigma_z, and show that they do not commute.
