Method of Isochrons and Gravity Flashcards
What are the first three steps in the method of isochrons?
- Take samples of several different minerals from rock
- Choose decay system such that D and R are same element, N is different
- Measure isotopic ratios D/R and N/R for each mineral sample by mass spectrometry and plot graphs
What are the last 3 steps in the method of isochrons?
- If data lies on straight line, system has been closed, and M gives age of rock, C gives initial ratio
- Scatter indicates poor ‘closure’, i.e. that isotopes have been exchanged with the environment
- Line of best fit through many points reduces random error
What is the closure temperature?
Diffusion of a mineral behaves exponential with temperature - diffusion starts after specific temp (closure temp)
What does it mean if a rock is heated past the closure temperature since its formation?
Rock may have exchanged isotopes with its environment.
What are 4 widely used radiometric dating systems?
- Rubidium-Strontium
- Potassium-Argon
- Uranium-Lead
- Thorium-Lead
What are N, D and R equal to for the Rb-Sr system? What can we assume here? What is this system used for?
- N = Rubidium-87
- D = Strontum-87
- R = Strontium-86
Sr-87/Sr-86 (now)= Sr-87/Sr-86 (0) + Rb-87/Sr-86 (now) * λt
Used for ancient rocks as has very long half life.
What are N, D and R equal to for the K-Ar system? What is effective here and what is the closure temp like? What is this system used for?
- N = Potassium-40
- D = Argon-40
- R = Argon-36
can have effective λ(effective). Closure temp relatively low
Used for determining thermal history of a rock
What are N, D and R equal to for the U-Pb system? What is this system used for?
-N = Uranium-238
-D = Lead-206
-R = Lead-204
OR
-N = Uranium-235
-D = Lead-207
-R = Lead-204
Can determine age of rock and time at which disturbance causing system to lose or gain lead might have occurred.
What are N, D and R equal to for the Th-Pb system? What is this system used for?
- N = Thorium-232
- D = Lead-208
- R = Lead-204
Provide further cross checking with Uranium method
What is Newtons law of gravitation?
F = GMm/(|r1-r2|^2) * (r1-r2)/|r1-r2|
What is the integral version of newtons law of gravitation?
F(r) = triple integral over u of Gmρ(r1)*(r1-r)/(|r1-r|^3) dr1
What can we infer from knowing the density or the force on object u?
- Knowledge of ρ leads to knowledge of F
- Knowledge of F does not lead to knowledge of ρ
What is the integral equation for the gravitational potential energy?
V(r) = triple integral over u of -G*ρ(r)/|r1-r| dr1
What is the equation for the acceleration of a test mass due to gravity?
g(r) = -∇V(r)
What are the key points to consider when calculating the gravity due to a spherical shell?
- Gravity inside uniform spherical shell g(r) = 0
- Gravity outside of spherical shell is equivalent to having a point mass at centre of the shell
