A hydrogen atom in its fourth excited state emits a photon with a wavelength of nm. What is the atom’s maximum possible orbital angular momentum (as a multiple of ) after the emission?
Maximum possible orbital angular momentum is .
Fourth excited state means
Using Formula , , where is the wavelength , is rydberg constant , is the final orbital of electron , is the initial orbital of electron , is atomic no
Now for hydrogen
Now , Putting all the values in the formula we get
Solving it we get
It means transition
Now , we know that orbital angular momentum is
Now after emmision we have
So, the maximum angular momentum comes out to be
The 1997 Nobel Prize in physics went to Steven Chu, Claude Cohen-Tannoudji, and William Phillips for their development of techniques to slow, stop, and “trap” atoms with laser light. To see how this works, consider a beam of rubidium atoms (mass ) traveling at after being evaporated out of an oven. A laser beam with a wavelength of is directed against the atoms. This is the wavelength of the transition in rubidium, with being the ground state, so the photons in the laser beam are easily absorbed by the atoms. After an average time of , an excited atom spontaneously emits a 780-nm-wavelength photon and returns to the ground state.
a. The energy-momentum-mass relationship of Einstein’s theory of relativity is . A photon is massless, so the momentum of a photon is . Assume that the atoms are traveling in the positive x-direction and the laser beam in the negative x-direction. What is the initial momentum of an atom leaving the oven? What is the momentum of a photon of light?
b. The total momentum of the atom and the photon must be conserved in the absorption processes. As a consequence, how many photons must be absorbed to bring the atom to a halt?
NOTE Momentum is also conserved in the emission processes. However, spontaneously emitted photons are emitted in random directions. Averaged over many absorption/emission cycles, the net recoil of the atom due to emission is zero and can be ignored.
c. Assume that the laser beam is so intense that a ground-state atom absorbs a photon instantly. How much time is required to stop the atoms?
d. Use Newton’s second law in the form to calculate the force exerted on the atoms by the photons. From this, calculate the atoms’ acceleration as they slow.
e. Over what distance is the beam of atoms brought to a halt?
Suppose you put five electrons into a -wide one dimensional rigid box (i.e., an infinite potential well).
a. Use an energy-level diagram to show the electron configuration of the ground state.
b. What is the ground-state energy that is, the total energy of all five electrons in the ground-state configuration?
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