Geological Time and Radiometric Dating

Question 1

What are the two numbers which specify an element?

Answer 1

Atomic Number Z - specifies element

Atomic Mass A - specifies isotope

Question 2

What happens to the atomic number and the atomic mass in alpha decay?

Answer 2

Z -> Z-2, A-> A-4

Question 3

What happens to the atomic number and the atomic mass in beta decay?

Answer 3

Z -> Z+1, A -> A

Question 4

What is the equation for the number of nuclei over time?

Answer 4

N(t) = N(0)*exp(-λt)

Question 5

What is the equation for an atoms half life?

Answer 5

T(1/2) = ln(2)/λ

Question 6

What are the 4 steps in the formation of the Earth?

Answer 6

1-Nebular dust gathers and begins to collapse
2-Protostar forms out of gas, and planetesimals form out of dust, as cloud condenses into pancake shape
3-Planetesimals grow to about 1000km and star is formed
4-Accretion of planetesimals by collision causes growth of larger bodies

Question 7

How long does this process take approximately?

Answer 7

~10^8 years.

Question 8

What are the three sources of heat during the planet formation?

Answer 8

• Kinetic energy from collisions
• Gravitational contraction
• Radioactivity, decay processes

Question 9

What happens if the heat generation in a planet is more than the heat escape?

Answer 9

The planet turns molten.

Question 10

What happens if a planet turns molten?

Answer 10

Heavier elements pull to the centre, and the iron catastrophe happens!

Question 11

What happens in the iron catastrophe? (3 steps)

Answer 11

• Heat melts Fe
• Dense molten Fe falls towards core
• Releases G.P.E

Question 12

What can we use the iron catastrophe for with the Earth?

Answer 12

Whole planet at some point was a molten rock, so everything was mixed up with equal isotopes everywhere. Can use this as time 0 for our rock dating.

Question 13

What is the definition of a rock?

Answer 13

A rock is a mixture of minerals, possibly with organic and inorganic constituents.

Question 14

What is the definition of a mineral?

Answer 14

Naturally occurring inorganic substance, with well defined crystal structure. Impurities often present, useful for radiometric dating.

Question 15

What is the method of radiometric dating?

Answer 15

• Exploit radioactive decay of an element with known decay constant
• Take sample from rock of specific mineral
• Use mass spectrometer to measure ratios between different isotopes

Question 16

How do you get an equation for age of a rock?

Answer 16

Rearrange the equation for the number of nuclei for t.

Question 17

What is the equation for the daughter atom D when parent N decays?

Answer 17

D(t) = N(0) - N(t)

Question 18

What is the final equation for D(t)?

Answer 18

D(t) = N(t)*(exp(λt)-1) + D(0)

Question 19

What 3 things do we assume for D?

Answer 19

D(0) = 0
D is a stable isotope
D cannot leave system

Question 20

How can we find D(0)?

Answer 20

Find another stable element of D called R which does not decay, and so R(t) = R(0)

Question 21

How can we use a graph to work out the age of something?

Answer 21

Plot D/R against N/R, and find the gradient equals (exp(λt)-1)

Question 22

State 4 things to consider when picking a radiometric dating system.

Answer 22

• Different isotopes of same element react identically under physical and chemical influences
• Different minerals have different abundances
• Signal-to-noise of measurement can be low
• Ensure system is closed