1. The nucleus of a hydrogen atom is a single proton, which has a radius of about 1.0 10-15 m. The single electron in a hydrogen atom normally orbits the nucleus at a distance of 5.3 10-11 m. What is the ratio of the density of the hydrogen nucleus to the density of the complete hydrogen atom?
(density of nucleus / density of atom) =

2. In a Rutherford scattering experiment a target nucleus has a diameter of 1.4 10-14 m. The incoming has a mass of 6.64 10-27 kg. What is the kinetic energy of an particle that has a de Broglie wavelength equal to the diameter of the target nucleus? Ignore relativistic effects

3. A hydrogen atom is in its n = 6 excited state. Determine, according to quantum mechanics, each of the following:
(a) The total energy
eV=
(b) The magnitude of the maximum angular momentum the electron can have in this state
J s=
(c) The maximum value that the z component of the Lz of the angular momentum can have
J s =

Hi

For 1.

Density = Mass/Volume
Volume of a sphere = 4/3*pi*r^3

For 2.

De Broglie Wavelength = h/mv

work out the v you need

then KE = 1/2 mv^2

I don't know why you needed help with the first 2 if you're studying quantum mechanics ;p

3. a)

E = -13.6(1/n^2)eV

For the rest, I've found a page about angular momentum of electrons in Hydrogen atom.

You should learn something.

http://galileo.phys.virginia.edu/classes/252/Angular_Momentum/Angular_Momentum.html