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In a Compton effect experiment with incident X-ray of wavelength 0.060\text{ \AA}, one recoil electron had energy 4100\text{ eV}. Calculate the corresponding angle of scattering and the wavelength of the scattered radiation (Standard formulae may be assumed.)
What is the value of the spin of the electron and the corresponding magnetic-moment? Can that be considered as arising from the classical case of rotation of a finite rigid charged body about its axis? Give reasons for your answer.
Set up Schrodinger's equation for a one dimensional harmonic oscillator. Assuming that the solution is of the from \psi = A e^{-\alpha x^2} f(x) where \alpha is a constant and f(x) is a polynomial in x, find the energy eigen values and the ground state eigenfunction. Comment on the relation between the ground slate energy and Heisenberg's uncertainty principle.
State the important points in Bohr's theory of the hydrogen atom winch depart from classical ideas. Flow is the idea of Bohr orbits changed in Schrodinger's wave mechanics?
State de Brogue hpotliesis and use it to deduce the energy levels of a particle in a one-dimensional box. Calculate the mean energy per electron at 0\text{ K} if electrons arc enclosed in a long-chain molecule of length 50\text{ \AA}.
In a Compton scattering the angle of scattering was 30^\circ while the angle of recoil was 60^\circ. Calculate the energy of the incident photon taking the formulae you use as given.
In a hydrogen atom the electron is replaced by a muon whose mass is 200 times that of the electron and charge is the same as that of the electron. Calculate the Ionization potential on the basis of Bohr's model.
Photoelectron are liberated by ultraviolet light of wavelength 3000\text{ \AA} from a metallic surface for which the photoelectric threshold is at 4000\text{ \AA}. Calculate the De Broglie wavelength of electrons emitted with maximum kinetic energy.
Write down Schrodinger's equation in one-dimension and explain the significance of the eigenvalues and eigenfunction of this equation. Solve the Schrodinger's equation if the potential function V is given as V(x) = V_e(\text{a constant}) for |x| < a/2 = 0 for |x| > a/2 State the boundary conditions you use along with their justification (In the solution consider particles incident from one side only.) If he total energy F < V_0 show that there is an important difference with classical mechanics. Explain with the help of the uncertainty principle that E < V_0 does not mean that the kinetic energy is negative.
Derive Schrodinger equation for a linear harmonic oscillator, and determine its eigenvalue and eigenfunctions. Discuss the significance zero point energy.
State and explain Einstein's photoelectric emission equation, Distinguish between extrinsic and intrinsic photo electric effects. What is "quantum field"? On what factors does the quantum yield depend?
An electron moves with a speed of 10^{3}\text{ m/sec}, accurate to 0.008\%. Find the accuracy with which the position of the electron can be located.
Define Compton wavelength for an electron. Calculate in electron-volts the photon energy corresponding to radiations of the Compton wavelength. What light does the Compton effect throw on the nature of X-rays?
State and explain Heisenberg uncertainty principle using situations where one of the parameters is (a) liner distance x (b) angle \phi (c) energy E. Prove that according to the principal the presence of an electron within the atomic nucleus is not possible.
Compare the energy of a photon with that of a neutron when both are associated with wavelength of 1\text{\AA}.
Construct solutions of Schrodinger equation for a particle moving the potential \begin{aligned} V(x) &= 0 & \text{for } x < 0 \\\\ &= V_0 & \text{for } x > 0 \end{aligned} Deduce the reflection coefficient for particles incident from left to right (i.e. from negative to positive x regions) with energy E > V_0. Do you expect any reflection for particles of same energy incident from right to left? Explain qualitatively.
Find the Fermi energy in eV of electrons in sodium(_{11}^{23}\text{C Na}), given its density to be 0.97\text{ g cm}^{-3}. Treat the electrons as a free gas.
The stopping potential for electrons emitted from a metal, due to photoelectric effect, is found to be 1\text{ volt} for light of 2,500\text{ Angstrom units}. Calculate the work function of the metal in electron volts.
What is the importance of study of deuteron? Obtain the solution of Schrodinger equation for ground state of deuteron and show that deuteron is a loosely bound system.
$. Interpret your result.