Atomic spectra

In a Rutherford scattering experiment, an alpha particle (charge = +2e) heads directly toward a gold nucleus (charge = +79e). The alpha particle has a kinetic energy of 5.0 MeV when very far (r to infinity) from the nucleus. Assuming the gold nucleus to be fixed in space, determine the distance of the closest approach. Use conservation of energy with PE = k2q1q2/r).

Schrodinger equation for harmonic oscillator

The schroedinger equation for harmonic oscillator can be written: (the attachment) - Write and formally differentiate each term to get the second derivative with respect to X. Put it all into the equation as shown and you will see that there will be an infinite number of possible solutions, with progressively higher powers of x in the wave function. Write the first three (lowest three in order of powers of X) wave functions that solve the equation. (that is, determining values for the A's in each of the possible solutions.) (Hint: hermite poynomials)

Simple Harmonic Motion

The period of oscillation of a spring-and-mass system is 0.50 seconds and the amplitude is 5.0cm. What is the magnitude of the acceleration at the point of maximum extension of the spring?

The Doppler Effect

A source of sound waves of frequency 1.0 kHz is stationary. An observer is traveling at 0.50 times the speed of sound. What is the observed frequency if the observer moves toward the source? What is the observed frequency if the observer moves away from the source instead?

The Lorentz transformation

A clock in the moving coordinate system reads t'=0 when the stationary clock reads t=0. If the moving frame moves at a speed of 0.800c, what time will the moving clock read when the stationary observer reads 15.0 hr on her clock? Using lorentz transformation Thanks for your help.