Momentum: laser beam and photons

In summary, the beam of 109 rubidium atoms traveling at the speed of sound would be stopped by absorbing 61545 photons per second.
  • #1
KL90
7
0

Homework Statement


A rubidium atom traveling at the speed of sound absorbs photons from an oncoming laser beam Each photon can be viewed as a tiny ping pong ball having momentum 7.79 x 10-28 Nt/sec. The atom absorbs a photon which is then reradiated in any direction. Hence, on average each photon absorption /reemission reduced the atom's momentum by a photon momentum. (Use 87Rb and speed of sound = 330 m/sec)
a) How many photons must an atom absorb and reradiate in order to be stopped?

b) What is the deceleration experienced my the atom if it can absorb and reradiate a photon every 2.5 x 10-8 sec?

c) What distance does it take to stop an atom?

d) How many photons/sec are required to stop a beam of 109 atoms/sec?


Homework Equations


F=ma=[tex]\Delta[/tex]p/time
x = x0 + u0t + 1/2at2


The Attempt at a Solution



a) # photons = atom momentum / photon momentum
= (87 x 1.67x10-24/1000) (330m/sec)/ 7.79 x 10-28
= 61545 photons

b) a= F/atom mass=[tex]\Delta[/tex]p/(time x Rb mass)=photon momentum/(time x Rb mass)
= 7.79 x 10-28 / [2.5 x 10-8 x (87x1.67x10-24/1000)]
= 2.1 x 105 m/sec2

c) x = x0 + u0t + 1/2at2
t = #photons absorbes x time to absorb 1 photon
= 61545 x 2.5 x 10-8
= 1.54 x 10-3 sec

x = 330t + 1/2 (2.1 x 105) t2
= 0.76m

d) Unsure --> attmept --> 109 / 61545
= 16248 photons/sec
 
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  • #2
KL90 said:

The Attempt at a Solution



a) # photons = atom momentum / photon momentum
= (87 x 1.67x10-24/1000) (330m/sec)/ 7.79 x 10-28
= 61545 photons

b) a= F/atom mass=[tex]\Delta[/tex]p/(time x Rb mass)=photon momentum/(time x Rb mass)
= 7.79 x 10-28 / [2.5 x 10-8 x (87x1.67x10-24/1000)]
= 2.1 x 105 m/sec2
a & b look good :smile:
c) x = x0 + u0t + 1/2at2
t = #photons absorbes x time to absorb 1 photon
= 61545 x 2.5 x 10-8
= 1.54 x 10-3 sec

x = 330t + 1/2 (2.1 x 105) t2
= 0.76m
Watch the +/- signs here. Are the atoms accelerating or decelerating?

d) Unsure --> attmept --> 109 / 61545
= 16248 photons/sec

Hmmm, no. Think in terms of units.

You'd need 61545 photons per Rb atom to stop them all.
The beam has 109 Rb atoms per second.
 
  • #3
c) x = 330t - 1/2 (2.1 x 105) t2
since it is decelerating, the acceleration would be negative.

d) 109 Rbatoms/sec x 61545 photons/Rb atom = xphotons/sec

Thanks a lot!
 

1. What is momentum in relation to a laser beam?

Momentum is a physical quantity that describes the motion of an object. In the context of a laser beam, it refers to the amount of force that the beam has as it travels through space.

2. How is momentum related to the photons in a laser beam?

Photons are the fundamental particles that make up a laser beam. They have a specific amount of momentum that is dependent on their wavelength and frequency.

3. Can momentum be transferred between laser beams and other objects?

Yes, the momentum of a laser beam can be transferred to other objects through the process of absorption or reflection. This is the principle behind laser propulsion and other applications of laser technology.

4. Is momentum conserved in a laser beam?

According to the law of conservation of momentum, the total momentum of a system remains constant unless acted upon by an external force. This means that the total momentum of a laser beam will remain constant unless it is influenced by external factors like gravity or collisions.

5. How is the momentum of a laser beam measured?

The momentum of a laser beam can be measured by using a device called a momentum meter. This device uses a force sensor to measure the amount of force exerted by the laser beam, which is then used to calculate its momentum.

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