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This is a page where I can broaden the context of a discussion and offer motivated students advanced material.
Arithmetic with units
- addition and subtraction: units don't change
2
kg + 3 kg = 5 kg
412 m - 12 m = 400 m
- consequence: units must be the same before adding or subtracting!
3.001 kg + 112 g = 3.001 kg + 0.112 kg = 3.113 kg
4.314 Gm - 2 Mm = 4.314 Gm - 0.002
Gm = 4.312 Gm
- multiplication and division: units multiply & divide too
3
m × 3 m = 9 m2
10 kg × 9.8 m/s2 = 98 kg m/s2
- consequence: units may cancel
5 g / 10 g = 0.5 (no
units!)
10.00 m/s × 39.37 in/m = 393.7 in/s
Converting Units
- 5 step plan for converting units
- identify the unknown, including units
- choose a starting point
- list the connecting conversion factors
- multiply starting measurement by conversion factors
- check the result: does the answer make sense?
- Common variations
- series of conversions
- example: Americium (Am) is extremely toxic; 0.02 micrograms is the allowable
body burden in bone. How many ounces of Am is this?
- converting powers of units
- converting compound units
- starting point must be constructed
- using derived units as conversion factors
- mass fractions (percent, ppt, ppm) convert mass of sample into mass of component
- density converts mass of a substance to volume
- velocity converts distance traveled to time required
- concentration converts volume of solution to mass of solute
http://antoine.frostburg.edu/chem/senese/101/measurement/index.shtml#arithmetic with units
All substances are made up of matter and the fundamental unit of matter is the atom. The atom constitutes the smallest
particle of an element which can take part in chemical reactions and may or may not exist independently.
The history of the discovery of the atomic structure is outlined below.
- John Dalton (1808) proposed the Atomic Theory. According to Dalton, matter is made up of tiny particles called
atoms. The atom is the smallest particle of matter that takes part in a chemical reaction. Atoms are indivisible and cannot
be created or destroyed. Further, atoms of the same element are identical in every respect.
- J. J. Thomson (1897) discovered electrons in Cathode Ray experiments. According to Thomson, atoms are divisible.
Atoms contain very tiny negatively charged particles called electrons.
- E. Goldstein (1900) discovered protons in Anode Ray experiments. According to Goldstein, atoms contain positively
charged particles called protons. Since atoms contain negatively charged particles, they must contain positively charged particles
for them to be electrically neutral.
- E. Rutherford (1911) discovered the nucleus and provided the basis for the modern atomic structure through his
alpha particle scattering experiment. According to Rutherford, the atoms is made of two parts: the nucleus and the extra-nuclear
part. His experiments proved that the atom is largely empty and has a heavy positively-charged body at the center called the
nucleus. The central nucleus is positively-charged and the negatively-charged electrons revolve around the nucleus.
- James Chadwick (1932) disovered neutrons. According to Chadwick, atoms contain neutral particles called neutrons
in their nucleus along with the subatomic particles (i.e., electrons and protons).
- N. Bohr (1940) provided the modern concept of the atomic model. According to Bohr, the atom is made of a central
nucleus containing protons (positively-charged) and neutrons (with no charge). The electrons (negatively-charged) revolve
around the nucleus in different imaginary paths called orbits or shells.
- Atomic number of an element is the number of protons in the nucleus of an atom. Since atoms are electrically neutral,
the number of protons equal the number of electrons in an atom.
- Atomic weight (or relative atomic mass) of an element is the number of times an atom of that element is heavier
than an atom of hydrogen. The atomic weight of hydrogen is taken to be unity [1].
- Mass number of an element is the sum of the number of protons and neutrons in the nucleus of an atom.
http://www.syvum.com/cgi/online/serve.cgi/squizzes/chem/atomic1.html
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