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Chapter 41: Q. 23 (page 1207)

A 1.0mW helium-neon laser emits a visible laser beam with a wavelength of 633nm. How many photons are emitted per second?

Short Answer

Expert verified

No of photons emitted per second are

N=3.34×1015

Step by step solution

01

Given information

We have given that,

P=1mW=10-3Wλ=633nm=633×10-9m

We have to find the no, of photons emitted per second.

02

Simplification

Since P=0.0010W, the laser light emits Elight=0.0010Jof light energy per second.

This energy consists of Nphotons. The energy of each photon is

E=hf=hcλ=3.14×10-19J

As Elight=NEphoton,the no. of photons is

N=ElightEphoton=0.0010J3.13×10-19J=3.2×1015

So, the photons are emitted at the rate of3.2×1015s-1.

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Most popular questions from this chapter

Three electrons are in a one-dimensional rigid box (i.e., an infinite potential well) of length 0.50nm. Two are in the n=1state and one is in the localid="1649073297418" n=6state. The selection rule for the rigid box allows only those transitions for which ∆nis odd.

a. Draw an energy-level diagram. On it, show the filled levels and show all transitions that could emit a photon.

b. What are all the possible wavelengths that could be emitted by this system?

The 1997Nobel 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 mass1.4×10-25kg traveling at 500m/safter being evaporated out of an oven. A laser beam with a wavelength of 780nm is directed against the atoms. This is the wavelength of the 5s→5ptransition in rubidium, with 5s being 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 780nmwavelength photon and returns to the ground state.

a. The energy-momentum-mass relationship of Einstein’s 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’s second law in the form F=∆p/∆tto 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?

List the quantum numbers, excluding spin, of

(a) all possible 3p states and

(b) all possible 3d states.

The ionization energy of an atom is known to be 5.5eV. The emission spectrum of this atom contains only the four wavelengths 310.0nm,354.3nm,826.7nmand 1240.0nm. Draw an energy-level diagram with the fewest possible energy levels that agrees with these experimental data. Label each level with an appropriate lquantum number. Hint: Don’t forget about the l→selection rule.

A hydrogen atom is in the 2p state. How much time must elapse for there to be a 1.0% chance that this atom will undergo a quantum jump to the ground state?
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