Question : A particle in one dimension is subject to a force$$ F = -k x +{ \lambda\over x^3} $$ Find the potential energy and the exact period of oscillations for$\lambda = 6ka^4, E= 5k a^2$.
Inkjet Printer
If an ink drop has a mass of $50\times10^{-9}$g and is given a charge of $-200\times 10^{-15}$ C, find vertical displacement in an inkjet printer with 3keV deflection potential, 3mm plate separation and 15 mm deflection plate length. The nozzle ejects the drop with velocity 25 m sec$^{-1}$ and leaving edge of the deflection plate is at a distance 15 mm from the paper.
ANS:: 2.16mm
$\newcommand{\ket}[1]{\vert #1\rangle}\newcommand{\matrixelement}[3] {\langle#1\vert#2\vert#3\rangle}$Question :: Construct the spin matrices for a spin half particle in the basis in which $S_z$ is diagonal.
Show that the probability that electron in the ground state of hydrogen atom will be found outside the classical region is $13e^{-4}$. It is given that the normalized radial wave function of the electron, in the ground state, is $$ R_{10}({r}) = 2 \left(1\over a_0\right)^{3/2} \exp(-r/a_0) $$ where \(a_0=\frac{\hbar^2}{me^2}\) is the Bohr radius and the energy levels of H atom are given to be \(E_n= -\frac{e^2}{2a_0n^2}\)
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