00:01
Hi, in this question we have a star having radius r given as 8 .40 into 10 raised 2 power 8 meter and has a peak wavelength lambda given as 682 nanometer.
00:18
So in the spectrum of its emitted radiation.
00:22
Now in part a of this question, we have to find the energy of a photon with this wavelength.
00:29
Now, to calculate the energy of photon, we'll use the formula e equals to hc by lambda.
00:39
So we can write this as 6 .63 into 10 raised to power minus 34 into 3 into 10 raised to power 8 divided by 682 into 10 raised to power minus 9 meter as it is a nanometer.
00:56
So from here, we get the value of energy equals to 2 .916 into 10 raised 2 .9 jule per photon.
01:12
Now, moving on to the next part, part b of this question.
01:17
So in part b, we have to calculate the surface temperature of the star.
01:22
So the surface temperature can be calculated using wayne's displacement law.
01:26
So according to wayne's displacement law, the temperature t is equals to 2 .898 into 10 raised to power minus 3 divided by lambda.
01:41
So, t can be calculated as 2 .898 into 10 raised to power minus 3 divided by 682 .68 into 10 raised to power minus 3 divided by 682 into 10 raised to power minus 9, gives the value of temperature as 4249 .27 kelvin.
02:06
Now moving on to the third part, that is part c.
02:10
So in part c they're asking at what rate is energy emitted from the star in the form of radiation.
02:19
So we have to assume that the star is a black body that is the value of e is equals to 1.
02:26
Now, from stephen's blackbody equation, we can write that p by a is equals to epsilon sigma t raise 2 power 4.
02:45
So here we have to calculate the value of p, which is the rate at which energy is emitted...