Quantum physics & Atomic Physics Question

[yoshima]

Hi, I've been trying to figure these two questions out but they haven't beeen working.

1. A hydrogen atom is in its fifth excited state. The atom emits a 1090 nm wavelength photon. Determine the maximum possible orbital angular momentum of the electron after emission. Express your answer as multiples of hbar. (ans. 2.583e-34)

my procedure... know that
angular momentum(L) = sqaure root(l(l+1) * 1.0545e-34

since n=5. than l=4 sub that into the equation and get the anwser. but this is not working.

2. A certain electron microscope accelerates electrons to an energy of 60.5 keV. Calculate the wavelength of these electrons. If one can resolve two points separated by at least 55.0 wavelengths, what is the smallest separation (or the minimum-sized object) that can be resolved with this microscope?

my procedure: E=h*c/lambda solve for lambda and that would be the anwser. I converted the units to the appropritate ones and still this does not work. I also tried E=.5*m*v^2 solving for v and than solving for lambda that does not work either. for the second part you multiply 55 wavelengths with the lambda calculated. But this can not be done until lambda is right.

Any help would be great. Thanks

 

[Doc Al]

A few comments:
Prob 1: First, realize that the 5th excited state is n = 6. Second, find out what the final energy level is after the photon is emitted. (Use the photon wavelength.)

Prob 2: That equation is for the wavelength of a photon. Use the relativistic formula to find the momentum of the electron.

 

[yoshima]

for question 2: what is the relativistic formula ? The cousre does not cover relativity.

 

[Doc Al]

for question 2: what is the relativistic formula ? The cousre does not cover relativity.

If you don't cover relativity, then I don't see how you can do this problem. If you use the pre-relativistic equation KE = 1/2 m v^2 to calculate v, you will get a speed which is an appreciable fraction of the speed of light. (What speed do you get?) Thus relativity must be used to find the momentum.

What formulas are you given regarding this type of problem? You may find this page useful: http://hyperphysics.phy-astr.gsu.edu/hbase/debrog.html