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Chapter 41: Q. 11 (page 1206)

In FIGURE Q41.12,a photon with energy 2.0eVis incident on an atom in the pstate. Does the atom undergo an absorption transition, a stimulated emission transition, or neither? Explain.

Short Answer

Expert verified

The given statement is proved.

Step by step solution

01

Given Information 

We have to given a photon with energy2.0eV.

02

Simplify

Here, shows an energy difference between the p鈥�state and the lower s鈥�state. Know that the energy of a photon matches the energy difference between the p鈥�state and the lower s鈥�state. The atom may a stimulated emission transition, but it will not undergo an absorption transition.

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Most popular questions from this chapter

A hydrogen atom has l=2. What are the (a) minimum (as a multiple of h ) and (b) maximum values of the quantity Lx2+Ly21/2 ?

How many lines of atoms would you expect to see on the collector plate of a Stern-Gerlach apparatus if the experiment is done with
(a) lithium and

(b) beryllium? Explain.

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 鈥渢rap鈥� atoms with laser light. To see how this works, consider a beam of rubidium atoms (mass 1.4x10-25kg) traveling at 500m/safter being evaporated out of an oven. A laser beam with a wavelength of 780nmis directed against the atoms. This is the wavelength of the 5s鈫�5ptransition in rubidium, with 5sbeing the ground state, so the photons in the laser beam are easily absorbed by the atoms. After an average time of 15ns, an excited atom spontaneously emits a 780-nm-wavelength photon and returns to the ground state.

a. The energy-momentum-mass relationship of Einstein鈥檚 theory of relativity is E2=p2c2+m2c4. A photon is massless, so the momentum of a photon is p=Ephoton/c. 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鈥檚 second law in the form F=鈭�p/鈭�tto calculate the force exerted on the atoms by the photons. From this, calculate the atoms鈥� acceleration as they slow.

e. Over what distance is the beam of atoms brought to a halt?

Prove that the normalization constant of the 1sradial wave function of the hydrogen atom is localid="1650358688008" 蟺aB3-1/2, as given in Equations 41.7.

A hydrogen atom has orbital angular momentum 3.65脳10-34Js

a. What letter s,p,dorf describes the electron?

b. What is the atom鈥檚 minimum possible energy? Explain.
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