Search, filter, and study UPSC Civil Services & IFoS Physics past year questions with rigorous derivations, formulas, and step-by-step solutions.
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} ]
If ^{11}\text{Na} atoms in their ground state are placed in a region having electromagnetic radiation of frequency \nu = 1\cdot 0 \times 10^{10}\text{ Hz}, calculate the required magnetic field B at which the electromagnetic radiation will be in resonance with the Zeeman splitting.
The Stern-Gerlach experiment is a landmark experiment in quantum mechanics. Discuss about the most important findings of this experiment.
The quantum numbers of two 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 L\text{-}S coupling, find the possible values of L and J.
Distinguish between fluorescence and phosphorescence. Explain the mechanisms responsible for these phenomena. Discuss the applications of fluorescence and phosphorescence in the fields such as biochemistry, material science, etc.
Obtain the resonance condition of nuclear magnetic resonance spectroscopy. Write down at least three important applications.
(i) Discuss the importance of studying the isotope effect in rotational spectroscopy. (ii) If hydrogen is substituted by deuterium in hydrogen molecule, calculate the change in rotational constant B.
Why were silver atoms used in Stern-Gerlach experiment? Also, write the importance of this experiment.
(i) With suitable diagrams, explain the intensity distribution of spectral lines in vibrational-electronic spectra by using the Franck-Condon principle. (ii) Calculate the positions of the first two rotational Raman lines in the spectrum of \text{H}_2, if its bond length is 0\cdot 074\text{ nm}. [Given : ^{1}\text{H} = 1\cdot 673 \times 10^{-27}\text{ kg}]
The force constant of \text{HCl} molecule is 4\cdot 8 \times 10^5 \text{ dyne/cm}. Calculate the wave numbers of Stokes and anti-Stokes lines, when excited with a radiation of wavelength 4358 \text{ \AA}. [ Given, \mu_{\text{HCl}} = 1\cdot 61 \times 10^{-24} \text{ g} ]
Write the electronic configurations for carbon (C), nitrogen (N) and oxygen (O) atoms, and then derive their ground states.
Explain the salient features of fluorescence and phosphorescence with the help of energy level diagram. Name a few applications of these phenomena in our daily life.
Experimental observation for the line spectrum of an atom shows that the separations between adjacent energy levels of increasing energy in a multiplet are in the ratio 3:5. By using the Landé interval rule, assign the quantum numbers L, S and J to these levels.
In case of pure rotational states, if the temperature will be doubled, then calculate the rotational quantum number corresponding to maximum population density. [ Assume that temperature is high ]
Draw the normal Zeeman pattern for {}^1\text{F}_3 - {}^1\text{D}_2 transition.
Find out the difference in frequencies of Lyman-alpha line in hydrogen and deuterium atoms.
From the pure rotational absorption spectra of a diatomic molecule (HF), the wave number difference between the consecutive rotational lines is found to be \Delta \bar{\nu} = 4050 \text{ m}^{-1}. Calculate the following : (1) Rotational constant (2) Moment of inertia (3) Distance between two atoms (bond length) [ Given, M_{\text{H}} = 1 \text{ u}, M_{\text{F}} = 19 \text{ u} ]
(i) Derive an expression for density of states for a free electron gas in one dimension. Hence, show its variation with energy for a one-dimensional metallic crystal. (ii) Where do you find the applications of free electron gas model?
A particle is described by the wave function \psi(x, t) = e^{i(kx-\omega t)}. (i) Is this wave function an eigenfunction corresponding to any dynamical variable or variables? If so, name the variable(s). (ii) Does this represent a ground state?
By applying the Schrödinger's equation to the ground state of hydrogen atom, determine the zero-point energy.