Quantum Mechanics Answers

For a hydrogen atom wave functions are written as

The hydrogen atom wave functions are written as

Using Maxwell’s equations, derive the wave equations for B.
Show that the wave equations admit plane waves for the electric and magnetic fields in free
space of the form

State Maxwell’s equation for the curl of the magnetic and the electric field in free space.
State the meaning of all the terms in the equations and identify the displacement current
density.

The hydrogen atom wave functions are written as

The nucleus of an atom has a mass of 3.8x10^-25 kg and is at rest. The nucleus is radioactive and suddenly ejects a particle of mass 6.6x10^-27 kg at a speed of 1.5x10^7 m/s. Find the recoil speed of the nucleus that is left behind.

A daredevil wishes to bungee-jump from a hot-air balloon 62.5 m above a carnival midway. He will use a piece of uniform elastic cord tied to a harness around his body to stop his fall at a point 13.0 m above the ground. Model his body as a particle and the cord as having negligible mass and a tension force described by Hooke's force law. In a preliminary test, hanging at rest from a 5.00-m length of the cord, the jumper finds that his body weight stretches it by 1.45 m. He will drop from rest at the point where the top end of a longer section of the cord is attached to the stationary balloon.

(a) What length of cord should he use?
m

(b) What maximum acceleration will he experience?
m/s2

If Nq electrons are contained in the volume at absolute zero temperature, describe how you would count the number of states/orbitals in the system.