I need help with question 5. 0 that the population will reach six million? (c) I

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I need help with question 5.

0 that the population will reach six million? (c) Is the population really growing exponentially? (5) All stars contain traces of metals which can be detected by analyzing their spectra. The heavier metals are almost exclusively made during extremely violent events such as supernova explosions. The debris from a supernova is widely scattered and is incorporated into other stellar bodies (stars and planets) during their formation. Some of the very heavy metals are (relatively) stable, while others are not. If we know the ratio in which these heavy metals are initially present and the half-life of an unstable metal, we can estimate the average ages of the supernovas that contributed to the sample. Since young galaxies have many more supernova explosions than older galaxies, this gives a rough idea of the age of the galaxy. The initial ratios are only known from theoretical calculations, so their values are a source of considerable uncertainty which must be taken into account in deriving these estimates. 232Th has a very long half-life and can be taken to be stable for the purpose of these calculations. 238U has a much shorter half-life of about 4.5 Gy. According to stellar nucleosynthesis models, the initial ratio of 238U to 232Th was between 0.56 and 0.79. The currently observed ratio of these two isotopes in star CS31082-001, a star in the Milky Way galaxy, is 0.18. Using these data, determine a range of possible ages for (6) While cooking a beef roast recently, I recorded the following data: the oven temperature otuure of the roast at various times (given as our galaxy

Explanation / Answer

C = Co e (-t)

At half life = 4.5 Gy of 238U:

Co / 2 = Co e (-t)

½ = e(- * 4.5)

* 4.5 = 0.693

= 0.154 Gy-1

Let initial 232Th amount present = R

Case 1:

Initial 238U present = 0.56 R

Final 238U present = 0.18 R

C = Co e (-t)

0.18 R = 0.56 R * e(-0.154 * t)

0.321 = e(-0.154 t)

0.154 t = 1.13

t = 7.37 Gy

Case 2:

Initial 238U present = 0.79 R

Final 238U present = 0.18 R

C = Co e (-t)

0.18 R = 0.79 R * e(-0.154 * t)

0.228 = e(-0.154 t)

0.154 t = 1.48

t = 9.6 Gy

Possible range of age for our galaxy = 7.4 Gy to 9.6 Gy

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