^{There are two types of charge: (+) & (-).   Like charges repel.   Opposite charges attract.}

^{3 Types of Radioactive Emission}
alpha particle: +2 charged particle (helium nuclei; He²⁺)
beta particle: -1 charged particle (high speed electron; e^1-)
gamma ray: high energy light (not deflected by (+) or (-) charge.)

Electrons
A cathode ray tube (gas discharge tube) is a partially evacuated glass tube with electrodes at each end. The pressure is lowered below 2 mmHg. (TV tubes are cathode ray tubes.) High voltage direct current produces radiation within the tube that are called cathode rays. So named because the rays travel from the negatively charged electrode (cathode) to the positively charged electrode (anode). The negative particles in the ray were eventually named electrons from the Greek word for amber (hlektron).   The movement of these rays in a cathode ray tube can be detected by materials within the tube that fluoresce or give off light.

Characteristics of Cathode Rays
1. Cathode rays travel in a straight line.
2. Cathode rays are attracted to the positive electrode.
3. Same type ray produced regardless of the cathode material.
4. Magnetic and electric fields "bend" the rays in the manner expected for negatively charged particles.
5. The metal plate exposed to the ray develops a negative charge.

In 1897 J. J. Thomson measured the ratio of the charge to mass of the electron: -5.6 x 10^-9 grams/coulomb. (The coulomb, C, is the SI unit of charge.)

In 1909 R. A. Millikan determined the unit charge of an electron to be -1.60 x 10^-19 C. The modern value is 1.6021773 x 10^-19 C.

Using these two values the mass of the electron is:   (1.60 x 10^-19 C)(5.6 x 10^-9 g/C) = 8.96 x 10^-28 kg

Modern mass: m_e = 9.109390 x 10 ^-31 kg or 5.485799 x 10 ^-4 amu.

Protons
When atoms lose electrons, they become positively charged.  An ion is a charged atom or group of atoms.  The ion formed from different elements all have different mass-to-charge ratios.  The smallest mass-to-charge ratio if formed from the hydrogen ion.  The hydrogen ion is the proton.  The mass of the proton is 1.67262158 x 10^-24 g.  The charge of the proton is equal but opposite in sign of that of the electron.

The Nucleus
Thomson proposed that atoms consisted of a large massive positively charged body with a number of small negatively charged electrons scattered throughout it. The total charge of the electrons exactly balanced the positive charge of the large mass, so the total electric charge was zero. This was called the plum pudding model of the atom.

Neutrons
In 1932 Chadwick discovers the neutron.  The charge of the neutron is 0 and the mass is 1.6749 x 10^-24g.

Summary & Recap of Atomic Structure:
The atom is 99.9% empty space.
The electrons, composing less than 0.1% of the atom’s mass, move around the nucleus.
In some atoms, the electrons are semi-free to move from one atom to another.
The atom is composed of three fundamental particles.
Proton and neutron are in the nucleus and the electron is outside the nucleus.
The mass of the atom comes predominantly from the nucleus.
The nuclear radius is approx. 10,000 times smaller than the radius of the entire atom.
The nucleus contributes less than 1% of the size of the atom, but 99.9% of the mass.
The electrons occupy most of the volume of the atom, but contribute very little mass.
Atoms are electrically neutral. Number of protons = number of electrons.
 

Particle	Relative Charge	Charge (C)	Mass (kg)	Relative Mass	Mass (amu)
Electron e-	-1	-1.60 x 10-19	9.11 x 10-31	1	0.0005485799
Proton p+	+1	+1.60 x 10-19	1.673x 10-27	1836	1.007276
Neutron  n	0	---	1.675x 10-27	1836	1.00866490

LENGTH
The SI unit of length is the meter (m), a unit about 10% longer than a yard.  One meter is 39.37 inches

VOLUME
Volume is the amount of space occupied by an object.  The SI unit for length is the meter and the SI-derived unit of volume is
 the cubic meter (m³ ).  One cubic meter is about 264.2  U.S. gallons.  Measurements of volume in the laboratory are normally
made in the liter (L).   A liter is the volume occupied by one cubic decimeter (dm³ ).

    1 L = 1 dm³ = 1 x 10^-3 m³             or 1 cm³ = 1 mL

MASS
Mass is the quantity of matter in an object.  The SI unit is the kg which is about 2.2 pounds.

TIME
The SI unit for time is the second.

PREFIXES FOR MULTIPLES OF SI UNITS
Some measurements are extremely small (bond distances in molecules) while others are extremely large (distances
between planets).  Prefixes are therefore utilized that modify these measurements in decimal fashion so as to make them
more convenient.
 

Some Common SI Prefixes
Multiple	Prefix	Symbol	Example equivalents using the  gram as the base unit
106	mega	M	1 Mg = 1 x 106 g = 1,000,000 g
103	kilo	k	1 kg = 1 x 103 g = 1000 g
10-1	deci	d	1 g = 1 x 101 dg = 10 dg
10-2	centi	c	1 g = 1 x 102 cg = 100 cg
10-3	milli	m	1 g = 1 x 103 mg = 1000 mg
10-6	micro	m	1 g = 1 x 106 mg = 1,000,000 mg
10-9	nano	n	1 g = 1 x 109 ng = 1,000,000,000 ng
10-12	pico	p	1 g = 1 x 1012 pg = 1,000,000,000,000 pg

SAMPLE PROBLEMS
Convert each of the following so that the power of ten is replaced by a prefix.
    1.    3.88 x 10^-2 g = ?              (3.88 cg)
    2.    1.72 x 10^-9 s = ?              (1.72 ns)
    3.    8.06 x 10³ L = ?              (8.06 kL)
    4.    6.95 x 10^-3 mol = ?          (6.59 mmol)

SAMPLE PROBLEMS
Convert each of the following.
    1.    157.63 kg =   ? g                (1.5763 x 10⁵ g)
    2.    2.385 x 10^-8 ns =   ? s           (2.385 x 10^-17 s)

All measurements have uncertainty.

Report measurements by recording all certain digits plus the first uncertain digit.

NUMBER OF SIGNIFICANT FIGURES
Rules of significant figures
A.  All Non zero digits are significant  (843.47 has five sig. fig.)
B.  Zeros -
         Leading zeros - not significant (zeros to the left of number; 0.0032 has two sig. fig.)
         Captured zeros - significant (zeros between non zero numbers; 2.003 has four sig. fig.)
         Trailing or terminal zeros- significant only if number contains a decimal point, otherwise not (zeros to right of
                                                            number;  9.0 has two sig. fig.)

Exact numbers - infinite number of sig. fig. (There are exactly 12 inches in 1 foot; both 12 and 1 are exact numbers and
therefore have an infinite number of sig. fig.)

Rules for significant figures in calculations
1. Multiplication/Division -
    the answer has same number of significant figures as the value in the operation with the least number of
   significant figures   (43.7 x 1.9932 = 87.10284; correct answer, 87.1,  has three sig. fig.)
2. Addition/Subtraction -
    the answer has same number of decimal places as the value in the operation with the least number of decimal places
    (27.35 + 1.4 = 28.75; correct answer, 28.8 has three sig. fig. because the least precise only has one decimal place.)

Exact numbers  have no bearing on the number of sig. fig. and are not considered when determining the number of
                             sig. fig. in an answer.

Rounding
If the first digit to be removed is less than 5, simply remove the unwanted digits.
The number 6.7495 rounded to two sig. fig. is 6.7 because 4 is less than 5.
If the first digit is 5 or more, increase the preceding digit by one.
The number 3.350 rounded to two sig. fig. is 3.4 because the first digit removed is 5.
The number 18.827 rounded to four sig. fig. is 18.83 because 7 is greater than 5.

ORDER of OPERATION:
Please             Parenthesis
Excuse            Exponents
My
Dear                Multiplication & Division
Aunt
Sally                Addition & Subtraction

SAMPLE PROBLEMS:
Perform the following operations and give answers in the correct number of significant figures.
A.     4.184 x 100.62 x (25.27 - 24.16) = ?            [467.]

B.   8.925 - 8.904 x 100 = ?            [0.24]
               8.925

C.     (9.04 - 8.23 + 21.954 + 81.0) / 3.1416 =?             [33.03]

D.       9.2 x 100.65  = ?                [75.]
          8.321 + 4.026

E.     0.1654 + 2.07 - 2.114 = ?                [0.12]

F.     8.27(4.987 - 4.962) = ?                [0.21]

G.        9 .5 + 4.1 + 2.8 + 3.175  = ?                 [4.9]
                        4

H.      9.025 - 9.024   x 100  = ?                [0.01]
              9.025

Atomic mass is related to the standard of carbon-12. By definition, an atom of carbon-12 has exactly 12 amu. Masses of all other atoms are relative to this scale.

1 amu = 1.66054 x 10^-24 g

This scale allows the assigning of masses to all other atoms.

EXAMPLE
On average, the V atom is 4.24 times more massive than carbon-12. What is the mass of V in amu and grams?
(4.24)(12) = 50.9 amu
(50.9 amu)( 1.66054 x 10^-24 g / 1 amu) = 8.45 x 10^-23 g

An estimation of an atom’s mass can be calculated by adding the number of protons and neutrons (both are close to 1 amu each). The mass from the electrons is negligible.

EXAMPLE
An aluminum atom has 13 protons and 14 neutrons so that its mass is approx. 27 amu.

The mass number (A) is the number of protons and neutrons in the nucleus.

A - Z = number of neutrons

Isotopes are atoms whose nuclei have the same atomic number but different mass numbers; that is they have the same number of protons but different number of neutrons.

Nuclide Symbols
  Mass # ->  1
                          H  <- Elemental symbol
 Atomic # ->  1

Atomic Mass
Percent abundance is the percentage of an isotope of an atom that exists in nature.

% abundance = (# of isotopes of an element/total # of isotopes)100

There are two naturally occurring isotopes of carbon on earth: 98.892% ¹²C and 1.108% ¹³C.

¹²C = 6 protons; 6 neutrons; 6 electrons

¹³C = 6 protons; 7 neutrons; 6 electrons

By international agreement, the current atomic mass standard is the pure isotope of C-12, which is assigned a mass of exactly 12 atomic mass units (12 u).  All weights on the periodic table are relative to this value.

If 1 atom of ¹²C has a mass of exactly 12 amu then the relative mass of 1 atom of ¹³C is 13.0035 amu.

Atomic mass
The atomic mass is the weighted average of the masses of the naturally occurring isotopes of that element.

Contribution of isotope = (fractional abundance) x (mass of isotope)

The atomic mass of carbon is:    (0.98892)(12 amu) + (0.01108)(13.00335 amu) =

                                                        = 11.867 + 0.1441 = 12.011 amu

All atomic masses are averaged because of isotopes.

The Mole
The SI unit for amount of substance is the mole. It is a counting quantity for particles such as atoms or molecules, or for other chemical entities. Thus, "the amount of water in a beaker" refers to the number of water molecules in the beaker and not the mass nor the volume of water. 

When the mole is used, the elementary entities must be specified and may be atoms, molecules, formula units of salts such as NaCl, ions, electrons, or other particles or specified groups of particles such as monatomic or polyatomic ions.

A mole is defined numberically as the quantity of substance in a sample that contains as many elementary entities as the number of atoms in exactly 12 g of C-12.  This value is 6.022 x 10²³.

The mass of one mole in grams is numerically equal to the molar mass. The mole is so defined that a sample of an element with a mass equal to its atomic mass in grams is one mole of that element.

1 mol of Na atoms = 22.99 g Na = 6.022 x 10²³ Na atoms

1 mol of CO₂ molecules = 44.01 g CO₂ = 6.022 x 10²³ CO₂ molecules

1 mol of MgCl₂ formula units = 95.21 g MgCl₂ = 6.022 x 10²³ MgCl₂ formula units

EXAMPLE
How many moles of Na are there in a 2.770 gram sample?

[2.770 grams][1 mol Na / 23.00 g] = 0.1204 moles of Na

EXAMPLE
How many moles of oxygen are contained in a 50.0 gram sample?

(50.0 g)(1mol / 32.00 g) = 1.56 moles O₂

EXAMPLE
How many mg of Ca are in 8.06 x 10^-5 moles?

[8.06 x 10^-6 mol Ca][40.08 g/mol] = 3.23 x 10^-4 g Ca

[3.23 x 10^-4 g Ca][1 x 10³ mg/g] = 3.23 x 10^-1mg