# Blackbody problem

1. Oct 4, 2005

### Sneil

Hi, im having trouble with the last question in my assignment. It's on blackbody radiation and total power per area and whatnot. those questions i was able to do fine, however when i came to this problem i was a little lost..

here it goes, i'll type the whole thing out..

"The most important energy source in so called main sequence stars is fusion of four protons into He nuclei.
A star has a radius r
How many he nuclei does the star produce per second if He production is the dominant energy source?
Use the Q value for the conversion 4H ->He to estimate the amount of raditation energy generated by hydrogen burning, and assume that the radiation energy output per second corresponds to the energy generated by hydrogen burning in a second."

any help would be greatly appreciated. thanks

-Neil

2. Oct 5, 2005

### Andrew Mason

Where did you get this problem? First of all, how do 4 protons fuse to become one He nucleus? Shouldn't it be 2 deuterons fuse to become a He nucleus?

You appear to be missing an essential piece of information: the surface temperature of the star. Without that, it is not possible to answer the question.

AM

3. Oct 5, 2005

### san_1420

Sure that's possible 4 H fuse to form 4He2 .
through Carbon Nitrigen Oxygen cycle
Well I can't remeber whole thing but you can find it in any text book.
Also a minimum temperature is required at core for this process ro take place
But surface temperature would be much lesser

4. Oct 5, 2005

### Sneil

sorry, i calculated surface temp to be 4990k

the question says turns to He (of atomic mass # 4)

i was just hoping for a formula i would be able to work with as i don't kow where to begin, but ill give the radius too if you want all the info. r=7.02*10^8 m

anyone able to help this early in the mourning?
thanks for the help, it is greatly apreciated

-Neil

Last edited: Oct 5, 2005
5. Oct 5, 2005

### Staff: Mentor

To be in equilibrium, the energy production in the star must equal the energy radiated, so

Egen = Number of reactions * Qreaction.

and one should have a formula for blackbody radiation, the Stefan-Boltzmann law E = ($\sigma T^4$) *A.

For He can be produced from 4 protons indirectly by the PP or CNO cycles.

http://csep10.phys.utk.edu/astr162/lect/energy/ppchain.html

http://csep10.phys.utk.edu/astr162/lect/energy/cno.html

or more generally

http://csep10.phys.utk.edu/astr162/lect/index.html

6. Oct 5, 2005

### Sneil

thanks man, im a little lost as to how i incorporate the radius, but ill figure it out

thanks

7. Oct 5, 2005

### Staff: Mentor

Surface area of a sphere, i.e. the star, of radius r is

A = 4$\pi r^2$.