Estimate the radiation pressure of your finger tip

In summary, the conversation involved estimating the radiation pressure and force exerted by a 100-W bulb at a distance of 5.0 cm from the center of the bulb. The formula for intensity was discussed, as well as the need to incorporate the surface area of a sphere and the number of photons and their respective momentum. The conversation also touched on the average wavelength of the light bulb and its relationship to its temperature. Ultimately, the correct solution was found to be Pressure = \frac{\frac{100 W}{4pi .05^2 m^2}}{c}.
  • #1
Queue
34
0

Homework Statement



Estimate the radiation pressure due to a 100-W bulb at a distance of 5.0 cm from the center of the bulb. Assume that light is complitely absorbed.

Estimate the force exerted on your fingertip if you place it at this point. Assume area of the fingertip to be 1.5 cm2.

Homework Equations



P = I/c
I = Power/(4*pi*d2)??

The Attempt at a Solution


I don't know how to solve for intensity. I think it should have units of W/m^2 so I would guess it would be 100/(4*pi*.05*.05) = Power/(4*pi*d2), since 4*pi*d*d would be the area of a sphere of radius d but I doubt it is correct.

For the second part it would just be the pressure I get in the first part times 0.00015 (1.5 cm2 in m2) for force.

Thanks in advance!
 
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  • #2
Yes, you need the surface area of a sphere radius=5cm.
Then you have the power/area at that distance ( since all the power from the bulb reaches the surface of this sphere)
Now you need to know how many photons/sec from the bulb and how much momentum/photon.

It's probably easier to do this in stages rather than just write a single equation - be carefull of the units.
 
  • #3
mgb_phys said:
Yes, you need the surface area of a sphere radius=5cm.
Then you have the power/area at that distance ( since all the power from the bulb reaches the surface of this sphere)
Now you need to know how many photons/sec from the bulb and how much momentum/photon.

It's probably easier to do this in stages rather than just write a single equation - be carefull of the units.

So am I correct in saying that pressure is intensity over the speed of light? If so, am I also correct in my formula for intensity?

I'm not quite sure how I work in momentum/second (momentum/photon and photons/second).
 
  • #4
The momentum of a photon is h / wavelength - where h is Planks constant.
The energy of a photon is h * frequency or h * speed of light / wavelength.

You will have to estimate an average wavelength for the light bulb (hint the filament is around 2-3000K + Wein's law)
 
  • #5
mgb_phys said:
The momentum of a photon is h / wavelength - where h is Planks constant.
The energy of a photon is h * frequency or h * speed of light / wavelength.

You will have to estimate an average wavelength for the light bulb (hint the filament is around 2-3000K + Wein's law)

How is this not giving me more than I need? The title's radiation is just about light not radiation per se.

My units work out if I have (100 W/(4*pi*.05*.05 m2)/c = 1.something*10-5 pascals which are the units I want for the question (thank you masteringphysics)
 
  • #6
100/(4*pi*.05*.05) is the intensity, ie the power/area at that distance.
To go from power to momentum you need to work out the number of photons and the momentum of each.
 
  • #7
mgb_phys said:
100/(4*pi*.05*.05) is the intensity, ie the power/area at that distance.
To go from power to momentum you need to work out the number of photons and the momentum of each.

Why can't I simply divide intensity by the speed of light which would make my units work out?

I submitted my solutions; Pressure = [tex]/frac{/frac{100}{4/pi .05^2}}{c}[/tex] worked.
 
Last edited:
  • #8
Queue said:
Why can't I simply divide intensity by the speed of light which would make my units work out?

I submitted my solutions; Pressure = [tex]/frac{/frac{100}{4/pi .05^2}}{c}[/tex] worked.

That should be [TEX]\frac{\frac{100 W}{4pi .05^2 m^2}}{c}[/TEX]

And for some reason this is coming out as mu_0*8/(2*pi*(.0447213595)) for some reason...
 

1. How is the radiation pressure of a finger tip estimated?

The radiation pressure of a finger tip is estimated by using the formula: P = (2.5 x 10^-6)(I/c), where P is the pressure in pascals, I is the intensity of the radiation in watts per square meter, and c is the speed of light in meters per second.

2. What is the intensity of radiation received by a finger tip?

The intensity of radiation received by a finger tip depends on various factors such as the type of radiation, distance from the source, and the material of the finger tip. However, on average, it is estimated to be around 0.02 watts per square meter.

3. Is the radiation pressure of a finger tip harmful?

No, the radiation pressure of a finger tip is not harmful. It is a very small amount of pressure that is not strong enough to cause any damage to the finger tip or the surrounding tissues.

4. How does the radiation pressure of a finger tip compare to other types of pressure?

The radiation pressure of a finger tip is much smaller compared to other types of pressure, such as air pressure or water pressure. It is even smaller than the pressure exerted by the weight of a single human hair.

5. Can the radiation pressure of a finger tip be measured?

Yes, the radiation pressure of a finger tip can be measured using specialized instruments such as radiation detectors or radiation pressure gauges. However, due to its small magnitude, it may be difficult to measure accurately without the use of sensitive equipment.

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