The average surface temperature of the sun is about 6000 K...

The average surface temperature of the sun is about 6000 K and its diameter is 1.4 x 10$^9$ m. The Stefan-Boltzmann equation gives the energy radiated as follows: radiation (J m$^{-2}$ s$^{-1}$) = $sigma T^4$ where $sigma$ = 5.67 x 10$^{-8}$ J m$^{-2}$ s$^{-1}$ K$^{-4}$ and T is temperature (K). Estimate how much of this radiation falls upon the Earth every second (you will need to look up some data on the size of our solar system). Estimate how much falls on your eyes every second. How many photons hit your eyes every second? (Assume they all have the same wavelength of 500 nm and the energy of a single photon is E = $hc/lambda$ where h is the Planck constant, c is the speed of light in a vacuum and $lambda$ is the wavelength - you will have to look up h and c).

Transcript

00:01 Hello students in this question we are given the information that the temperature of the surface of sun is equal to 6 ,000 kelvin and the diameter of sun is also given to us which is equals to 1 .4 multiplied by 10 to the power 9 meters the distance of sun to earth is also given to us which is equals to 1 .5 multiplied by 10 to the power 11 meters and the radius of human eye is equals to 25 multiplied by 10 to the power minus 3 meters.

01:13 So now we have to calculate how much radiation per second is falling on the earth.

01:25 Here, the radiation energy is equal to sigma t to the power 4 and the total radiation emitted by the sun.

01:44 Q is the total radiation emitted by the sun per second.

01:57 Is equals to sigma pi d s square t to the power four and the radiation received by earth per second will be equal to q over four pi r square where r is the radius so it will be equals to sigma pi d s square t to the power 4 over 4 pi radius of the earth square so it will be equal to on putting the values the values of sigma is 5 .67 multiplied by 10 to the power minus 8 multiplied by ds which is 1 .4 multiplied by 10 to the power 9 whole square and in temperature we can write 6 ,000 to the power 4 over 4 multiplied by radius is 1 .5 multiplied by 10 to the power 11 meters so there it is whole square on calculating it that radiation which is represented by i which is falling on the earth per second is equal to 1 .6 multiplied by 10 to the power 3 joule per meter square per second so this is a total radiation falling so it can be written as 1 .6 kilojoule meter per meter square per second now in the second part we have to calculate how much energy or the radiation is falling on the human high.

04:15 So here we have a formula e, which is the energy of each photon, is equal to hc over lambda.

04:27 So here on putting the values, it will be equals to h is 6 .6 multiplied by 10 to the power minus 34, multiplied by the speed of load...

Question

Please give Ace some feedback