Related Questions

In a two-electron atomic system having orbital and spin angular momenta $${l_1}{l_2}$$  and $${s_1}{s_2}$$  respectively, the coupling strengths are defined as $${\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}},\,{\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}},\,{\Gamma _{{l_1}{l_2}}}$$      and $${\Gamma _{{l_2}{s_1}}}.$$  For the jj coupling. scheme to be applicable, the coupling strengths must satisfy the condition
The resonance widths $$\Gamma $$ of $$\rho ,\,\omega $$  and $$\phi $$ particle resonances satisfy the relation $${\Gamma _\rho } > {\Gamma _\omega } > {\Gamma _\phi }$$   . Their lifetimes r satisfy the relation
The value of $$\oint {\Gamma \frac{{3{\text{z}} - 5}}{{\left( {{\text{z}} - 1} \right)\left( {{\text{z}} - 2} \right)}}{\text{dz}}} $$     along a closed path $$\Gamma $$ is is equal to (4πi), where z = x + iy and $${\text{i}} = \sqrt { - 1} .$$   The correct path $$\Gamma $$ is
With respect to the numerical evaluation of the definite integral $${\text{K}} = \int_{\text{a}}^{\text{b}} {{{\text{x}}^2}{\text{dx,}}} $$   where a and b are given, which of the following statements is/are TRUE?
I. The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral.
II. The value of K obtained using the Simpson's rule is always equal to the exact value of the definite integral.
Considering the problem of (linear) bending of beams according to the Euler-Bernoulli beam theory, if the beam is in equilibrium, then solving the equations governing the equilibrium of the Euler-Bernoulli beam is equivalent to minimizing the total potential energy.
In order to apply Bernoulli’s equation across two sections, we have to obtain it from Euler’s equation. What is the operation that needs to be carried out in order to obtain it from Euler’s equation?
While numerically solving the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + 2{\text{x}}{{\text{y}}^2} = 0,\,{\text{y}}\left( 0 \right) = 1$$     using Euler's predictor-corrector (improved Euler-Cauchy) with a step size of 0.2, the value of y after the first step is
The velocity v (in m/s) of a moving mass, starting from rest, given as $$\frac{{{\text{dv}}}}{{{\text{dt}}}} = {\text{v}} + {\text{t}}{\text{.}}$$   Using Euler forward difference method (also known as Cauchy-Euler method) with a step size of 0.1 s, the velocity at 0.2 s evaluate to
According to Euler's column theory, the crippling load of a column is given by $${\text{p}} = \frac{{{\pi ^2}{\text{E}}I}}{{{\text{C}}{l^2}}}.$$   In the Euler's formula, the value of C for a column with one end fixed and the other end free, is
The creep deformation rate of gamma iron is higher than alpha iron because the gamma iron is high-temperature phase.