2018年USAAAO长问题第3道

英文题目

3. [15 pt] Suppose that at some time in the very recent past all the hydrogen and helium (baryon density $$ρ_b = 4.2 × 10^{−31} g/cm^3$$ , about 75% hydrogen (=1 baryon) by mass and 25% helium (=4 baryons) by mass) in the universe had been instantly fused into iron in stars, and the released energy thermalized into black body radiation. (Note that the binding energy per nucleon of $$_{26}^{56}\textrm{Fe}$$ is 8.8 MeV and that of $$_{4}^{2}\textrm{He}$$ is 7.1 MeV.)

(a) [5 pt] Calculate the current temperature of this black body radiation.

(b) [5 pt] At what wavelength would the black body spectrum peak, and what region of the electromagnetic spectrum would this be?

(c) [5 pt] The mean bolometric luminosity per unit volume emitted by stars in the universe today is about $$3 × 10^8 L_{sun}/Mpc^3$$. How long would it takes stars at this rate to fuse all the hydrogen and helium in the universe? Compare to the present age of the universe.