How many photons does the sun emit in a second?
The following worksheet was used in companion with this post for chemistry students.
In this video, Brian Cox, repeats John Herschel’s famous experiment in Death Valley to determine the amount of energy the sun transmits to a given square meter of land.
From here, if you know the distance of the earth from the center of the sun, you can calculate the total amount of energy the sun emits in any direction by imaging the area of the sphere with this radius and multiplying by the amount of energy that heat up the can in one second.
The amount of energy delivered to the can is a type of calorimetry experiment:
The total energy from the sun at this diameter is calculated using:
Now, if we can estimate the energy of the average photon, we can estimate the number of photons this is.
Using this image (also below) of the distribution of photon wavelengths (obtained from a very interesting NASA space settlements website), we can estimate the “typical” wavelength of light coming from the sun.
The class estimated this to be between 0.7 and 0.8 microns or
We know that the energy of a photon can be calculated according to .
So there are approximately: photons leaving the sun every second!
The same kind of modeling (flux analysis) could be applied to determine the relative amount of energy that reaches other planets in the solar system (and thus exactly how much colder earth would be if it were twice as far away. The answer is that number of photons would scale as , so it would be four times colder!).
This analysis would also apply to stars that we view across the universe!
So the next question is, “How do we distinguish dimmer stars that are closer from brighter stars that are further away?”
The following worksheet can be used in companion with this material for multivariable calculus students.
Now that would be an interesting project for a multivariable calculus or an advanced chemistry student!