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Number of atoms trapped in an atom trap 
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#1
Mar1712, 01:42 PM

P: 24

1. The problem statement, all variables and given/known data
a group of atoms are confined in a point like volume in a laser based atom trap, the laser light causes each atom to emit 1.0 x 10^6 photons of wavelength 780 nm every second. the sensor has area of 1 cubic centimeter and measure the light intensity emanating from the trap to be 1.6 nW when placed 25 cm away from the trapped atoms. assuming each atom emits photons with equal probability in all directions, determine the number of trapped atoms. 2. Relevant equations 3. The attempt at a solution i honestly dont know where to begin with this problem, any guidance would be greatly appreciated, thanks 


#2
Mar1712, 02:52 PM

PF Gold
P: 3,188

The energy emitted by a single atom will be distributed homogeneously radially from it. Since your censor is 1 cm³ and inside an imaginary sphere of radius 25 cm, you can calculate how much % of the light (and hence power) coming from a single atom is received. Can you figure out how to continue? 


#3
Mar1912, 02:13 PM

P: 24

i found the frequency using f=v/[itex]\lambda[/itex] and then the power using hf emitted by each photon then multiyply that by the number of photons released per second, is this correct?



#4
Mar1912, 02:27 PM

PF Gold
P: 3,188

Number of atoms trapped in an atom trap



#5
Mar1912, 02:33 PM

P: 24

ah yes youre right my mistake, so i used E=hf and mulitpled it by 10^6 photons per second which would then in turn be equal to the power, correct?



#6
Mar1912, 02:48 PM

PF Gold
P: 3,188




#7
Mar1912, 02:55 PM

P: 24

first find the total intensity over the surface area of the sphere with radius 25cm and then find what fraction of that the sensor area is?



#9
Mar1912, 05:20 PM

P: 24

i have the ratio of the sensor area to the total sphere area, however how do i use that to find the emmitted photons in the sensor



#10
Mar1912, 05:33 PM

PF Gold
P: 3,188

This ratio is the percentage of the emitted photons that are received by the sensor, for all atoms. In the problem statement they give the information that the intensity in the sensor is 1.6 nW. You can determine the number of photons the sensor receives per second. Let's suppose (unrealistically) that the sensor receives 100 photons per second. And that you calculated that a single atom emitts 30 photons per second. Say you calculated the ratio we're talking about as being 1%. It means that the total source (or all atoms together) emitts 100 times more photons than then ones your sensor receives. Thus, in total 10,000 photons are emitted from the source per second. There's a very small last step, let's see if you can figure it out. :) 


#11
Mar1912, 05:52 PM

P: 24

i divided the number of photons hitting the sensor per second by the ratio we talked about to receive the total number of photons released from the source per second i then divided this by the number emitted per atom to find the number of atoms in the source. does this sound correct?



#12
Mar1912, 05:56 PM

PF Gold
P: 3,188




#13
Mar1912, 05:58 PM

P: 24

i calculated 1.95 x 10^12 atoms in the source, would you like my other numbers as well



#14
Mar1912, 05:59 PM

PF Gold
P: 3,188

I'm glad you've solved your problem. 


#15
Mar1912, 06:01 PM

P: 24

sounds good, thanks a bunch for the help glad i came here it was very useful!



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