Impossibility of photon absorption by a free electron. by superimpos- ing plots of the dispersion relations for photons and electrons, show that energy and momentum cannot both be conserved during the absorption or emission of a photon by a free electron, regardless of the initial velocity of the electron. 

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

Acompound machine is also called a machine. a. force b. simple c. complex d. directional

Carbon-14 is a radioactive element that undergoes beta decay. which force is responsible for allowing carbon-14 to become stable? electromagnetic gravitational weak nuclear strong nuclear