Explain l and ml

it's in Q#1 (as attached) I don't know how to explain why l amd ml (but not n) can cause energy degeneracy in one electron atom? (is it possible to explain the above in 3-4 lines? not just 1 line) (the deadline for this assignment has changed to Friday instead of Wednesday)

error?

it's Q# 2 (as attached) I had done question# 2 (as attached) but I don't understand why I cannot arrive at the answer given by the question? I don't know did i make a mistake somewhere or should I do more?

Electron Tunneling

I am given three unnormalized wavefunctions for the system: psi(x) = 100e^x for x<-4 psi(x) = 0.73 cos[(pi)x/40] for-44 I need to determine the probability of the wavefunction vs. x for this system from x=-10 to x=10 so that I can plot it. I have to comment on the probability of finding the particle outside of the box (x<-4 or x>4). Then I need to find the average kinetic energy of the particle between -4 and 4 using the kinetic energy operator and integral tables (Use the unnormalized function). Then I need to normalize the wavefunction in the region between -4 and 4.

Energy Levels of Hydrogen

(a) Assume that visible light refers to wavelengths between 400 nm and 700 nm. Which energy levels (if any) of the hydrogen atom bomb absorb visible light when making a transition to the next higher energy level? (b) If the relative probability of finding a hydrogen atom in its ground 1s state is I, the relative probability of finding it in any of the other state of energy En is {see attachment}. What is the relative probability at room temperature (T = 300 K) of finding a hydrogen atom in a state which can absorb visible light? Would you expect a room temperature sample of a gas of hydrogen atoms to be colouted? {see attachment}

Carbon dating of ancient bone

If one gram of Carbon 14 nuclides from an old bone is found to give off 0.478 decays (energy units) per minute, how old is this sample if originally the carbon-14 sample gives off 7.65 decays per minute, and the half life is 5715 years?