Exploring Astronomy: The Sun's Energy and Radioactive Dating
Dive into basic astronomy concepts such as the Sun's energy generation and radioactive dating, with calculations and discussions on the lifespan of the Sun and determining the age of a mysterious space rock.
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Presentation Transcript
Physics Circle November 16, 2022 Slides by Aakash Anantharaman An exercise in basic Astronomy
Astronomy and time Introductions and Overview Q.1 : Life of the Sun Q. 2 : Radioactive Dating
Q. 1 THE SUN !!! Current age : 4.603 billion years old Emits energy at 3.8 x 1026Watts Fusion (4H+ He + energy) (a) Using E = mc2, calculate the energy for each reaction. M(H+) : 1.7 10 27kg and M(He): 6.7 10 27kg. (b) Given the power, how many reactions (per second) are required to give the output? (c) What is the mass of Hydrogen used per second?
Hints C = 3 x 108m/s Power = Energy/time Conservation of energy : E(initial) = E(final) The first 3 parts of this question set you up with a quick exercise with basic algebra (which is what we re mostly using to explore this topic)
Solutions (a) 9e-12 J (b) 4.2e+37 reactions/s (c) 2.87e+11 kg
Q. 1 (continued) (d) Assume that the mass of the sun is 2 x 1030 kg, and 10 % of the total mass is used for fusion (as calculated previously). What is the total life of the sun? (e) Given the current age of the sun, how much longer will it burn and how much more does it have to burn? (f) Let one generation be 41.5 years. How many generations can humans stay till the sun burns out and we are forced to escape this solar system?
Solutions (d) 20 billion years (e) 15.397 billion years and 1.39e+29 kg left to burn
Discrepancy and explanation What is the actual total lifespan of the Sun? Is it the same as what we ve calculated? Why or why not? Based on the actual remaining time for the Sun, how many generations do we have? DISCUSS!
Q. 2 Radioactive Dating During one of your camping trips, you find a mysterious space rock amongst a barren patch of land. You are going to figure out its age using equipment you conveniently happen to have. This is the decay process that you will use to determine the age using relative concentrations. Problem developed by Dr. Allison Man
More background information A radioactive substance has a decay probability proportional to the number of atoms in it. It is given by the differential equation : dN = - Ndt dN is the change in number of atoms for change in time dt, as governed by the constant (- ). Q. 2 (a) Rearrange the equation and solve to obtain a result in terms of N. (Hint : at t(0), N = N0 (initial value))
Q. 2 (continued) Let s go back to the decay. 87Rb atoms are present in the space rock. Initially it had 87Rb0 atoms. Q. 2 (b) Using your equation from (a), write an equation for number of Rb-87 atoms now (you can use the notation 87Rbnowfor N ). Then write down an expression for the difference between the initial number Rb(0) and current number Rb(now) of Rb atoms.
Q. 2 (continued) Now going back to 87Sr. The difference calculated from the previous part is equal to the amount of Sr produced (let s call it 87Sr(prod)). The current total amount of Sr can be written by the equation 87Sr(now) = 87Sr(0) + 87Sr(prod). Q. 2 (c) Using this information and the equation obtained from the previous part, write an equation for 87Sr(now).
Solutions + Sanity Check !! (a) (b) (c)
Q. 2 (continued) In order to use the information we now have to determine the age of the space rock, we need to compare all the relative abundances with a stable isotope - let s use 86Sr as described in the following equation : Q. 2 (d) Calculate the relative abundances of 87Rbnowand 87Srnowif 87Sr0/86Sr0=2 and 87Rb0/86Sr0= 6 for t = 0,2 and 4 and = 1.543 x 10-11yr-1.
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