Large and small numbers -- scientific notation -- units etc.

1. Powers of ten, orders of magnitude

   10⁰ = 1

   10³ = 1,000 (kilo-, k)

   10⁶ = 1,000,000 (Mega-, M)

   10⁹ = 1,000,000,000 (Giga-, G)
   
   

   10^-3 = 1/1000 (milli-, m)

   10^-6 = 1/1, 000,000 (micro-, m)

   10^-9 = 1/1,000,000,000 (nano-, n)

   10^-12 = 1/1,000,000,000,000 (pico-, p)

   
   
   
2. Length or distance : basic scientific unit is a meter
   • 1 mile = 1.6 km
   • 1 angstrom (Å)= 10^-10 m -- the charcteristic dimensions of an atom, used to discuss the size of atoms, molecules etc.
   • 1 astronomical unit (AU)= 1.496x10¹⁰ m (93 million miles) -- the average distance from the earth to the Sun. This unit is used to measure distances in the solar system.
   • 1 light year = 9.461x10¹⁵ m (5.9x10¹² miles, or 633,000 astronomical units). This is the distance light travels in one year. The unit is used to measure distances between stars and galaxies.
   • 1 light second= 299,792 km (1 second at the velocity of light)
   
   
3. Mass : basic unit is the kilogram, originally defined as the mass of one liter (1000 cubic centimeters) of pure water
   • 1 kilogram (kg) = 2.2 pounds
   • mass of hydrogen atom = 1.66x10^-27 kg
   • mass of the Earth = 5.977x10²⁴ kg.
   
   
4. Time : basic unit is a second.
   • 1 year (length of time for the Earth to go around the Sun)= 3.155x10⁷ seconds.
   • Age of the Earth = 1.4x10¹⁷ seconds (4.55 billion years)

Time scales of phenomena being considered

• Atomic scale : 10^-14 - 10¹⁷ seconds... nuclear decay
• Human scale : years to hundreds of years ~3x10⁹ seconds
• geologic and astronomic scale : thousands to billions of years

Absolute dating: nomenclature

• Atom : smallest unit of an element, about 10^-10 m across, made up of protons, neutrons and electrons. The protons and neutrons are located in a small nucleus. The number of electrons define the chemistry of the atom.
• Element : specifies the number of protons in the nucleus. About 90 occur naturally and several more have been produced artificially.
• Isotope : specifies the total number of protons and neutrons in the nucleus. Isotopes can be either stable or radioactive. Radioactive isotopes decay to stable isotopes with widely varying half lives.

Radioactive isotopes used in geologic dating:

Parent --> Daughter : Half life

¹⁴C --> ¹⁴N : 5730 years

⁴⁰K --> ⁴⁰Ar : 1.25x10⁹ years

⁸⁷Rb --> ⁸⁷Sr : 4.88x10¹⁰ years

²³⁵U --> ²⁰⁷Pb : 7.04x10⁸ years

²³⁸U --> ²⁰⁶Pb : 4.47x10⁹ years

²³²Th --> ²⁰⁸Pb : 1.40x10¹⁰ years

¹⁴⁷Sm --> ¹⁴³Nd : 1.06x10¹¹ years