Quantum physics & Atomic Physics Question

In summary, the first question involves finding the orbital angular momentum of a hydrogen atom in its fifth excited state, and the second question involves using the relativistic formula to find the momentum of an electron accelerated to an energy of 60.5 keV. However, the course does not cover relativity, so it may not be possible to solve the second question without additional knowledge or formulas.
  • #1
yoshima
4
0
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
 
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  • #2
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.
 
  • #3
for question 2: what is the relativistic formula ? The cousre does not cover relativity.
 
  • #4
yoshima said:
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
 

1. What is quantum physics and how is it different from classical physics?

Quantum physics is the branch of physics that describes the behavior of matter and energy at a very small scale, such as atoms and subatomic particles. It is different from classical physics because it takes into account the principles of quantum mechanics, which include the concepts of uncertainty and wave-particle duality.

2. What is the principle of superposition in quantum physics?

The principle of superposition in quantum physics states that a particle can exist in multiple states simultaneously, until it is measured or observed. This means that a particle can be in two places at once, or have two different properties at the same time.

3. What is the Heisenberg uncertainty principle?

The Heisenberg uncertainty principle is a fundamental principle in quantum physics that states that it is impossible to know both the exact position and momentum of a particle at the same time. This is due to the wave-particle duality of particles, which means that the more precisely we know one property of a particle, the less precisely we can know the other.

4. How does quantum entanglement work?

Quantum entanglement occurs when two particles become connected in such a way that the state of one particle is dependent on the state of the other, even when they are separated by great distances. This phenomenon is still not fully understood, but it has been observed and has important implications for quantum information and communication.

5. What is the difference between atomic physics and nuclear physics?

Atomic physics deals with the properties and behavior of atoms, which are the building blocks of matter. It includes the study of atomic structure, atomic spectra, and atomic interactions. Nuclear physics, on the other hand, focuses on the structure and behavior of atomic nuclei, including nuclear reactions and nuclear energy production.

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