Monday, October 23, 2017

Summary of Atomic Theory

The 21st Century understanding of atomic theory is very effective in helping explain and predict how substances interact. It is the result of a growing body of knowledge that dates back centuries.


In the middle of the 5th Century BCE, Democritus proposed ideas that were correct in many ways. Democritus believed that all matter consisted of extremely small particles that could not be divided. He called these particles atoms from the greek word transliterated as atomos, which means "uncut" or "indivisible." 
He thought there were different types of atoms with specific sets of properties for the different substances in creation. The atoms in liquids, for example, were round and smooth, but the atoms in solids were rough and prickly. 
Though Democritus's ideas didn’t catch on, he was surprisingly accurate in his assumptions. Scientist of the 21st Century eventually concluded that many of Democritus’s ideas were correct, and they extended the understanding of atomic theory in stages that led to the current model.

John Dalton

Dalton proposed the theory that all matter is made up of individual particles called atoms, and in it, he identified several things that have lasted into the modern atomic theory:
  • All elements are composed of atoms.
  • All atoms of the same element have the same mass, and atoms of different elements have different masses.
  • Compounds contain atoms of more than one element.
  • In a particular compound, atoms of different elements always combine in the same ratios.

J. J Thompson
Thompson's experiments provided the first evidence that atoms are made of even smaller particles that have positive and negative charges.

Ernest Rutherford
Rutherford's model extended what was previously understood by identifying that atoms have a central, relatively dense (compared to the entire volume of an atom) nucleus around which electrons move. 

Niels Bohr

  • In Bohr's model, electrons move with constant speed in fixed orbitals around the nucleus.
  • Electrons must orbit the nucleus in one of several fixed, specific orbits, and each orbit represents a specific energy level.
  • The first orbital represents the lowest electron energy level, and the other orbitals represent progressively higher and higher energy levels.

Electron Cloud Model

  • Evidence following Bohr's work led to the understanding that the electrons do not orbit the nucleus like a planet.
  • While they do exist at specific energy levels and occupy orbitals, their position in the orbital is never 100% certain. They are somewhere in the orbital, but exactly where cannot be known specifically. Each orbital can be, therefore, conceived as an electron cloud. 

The progression of Atomic Theory in the modern era took place in various steps and stages. The resulting body of understanding results in a model of atoms that is highly effective and useful in understanding and predicting the behavior of substances.

Thursday, October 5, 2017

Solving Science Word Problems (and any other kind of word problem, too.)

Updated 2019-08-16

Throughout science, there inevitably comes a time when it is necessary to use some "known relationship" to figure out what happened or what might happen. In physics and chemistry, especially, this is the case, but sciences like sociology use "known relationships," such as population growth models, to explain or predict certain happenings. Business science looks at factors such as supply and demand or production cost vs sales price as means of maximizing profit.

In many, many cases, the "known relationship" is expressed as a mathematical equation. The relationship between the rate something happens and the amount of something produced is very common, so this discussion will use a couple of rate problems as its example.

In most general terms, the amount of something produced is equal to the rate of production times the amount of time production took place. For instance, in a displacement problem, rate is how far something moves in a given time and motion of an object is produced. In a general form a rate problem might look like this: 
O = R•t 
where O is the output, R is the rate, and t is the time.

So what is this process of solving science problem that will use rate problems as its example?

There are three steps to solving ANY science problem (or word problem of any kind, for that matter).

The following two examples will be used as the steps are discussed:

EXAMPLE 1: A baker's oven will hold only 1 pan of cookies, and each pain has space for 12 cookies. The baking time on cookies (including putting the dough on the pan) is 20 minutes. Therefore, the rate cookies are baked is 12 cookies per 20 minutes. How many cookies can be baked in 80 minutes? 
EXAMPLE 2: A car travels at an average rate of 20 MPH for 3 hours. How far does it go.

The first step is to write down what is asked for.  What are you supposed to find?
Example 1:
LOOKING FOR "How many cookies"
Example 2:
LOOKING FOR "How far does it go"
A student familiar with physics motion problems would see Example 2 as a "distance" problem and would use the distance equation variables. In such a case, R would be velocity, v, t would be time, t, and LOOKING FOR would be distance, d (or in some cases, s). 
The second step is to write down what's given and  find an equation that relates to the question.

Example 1:

Rate of baking  (R) = 12 cookies/20minutes
time (t) = 80 minutes

Intuition and general math instruction will lead you to a formula where…

Number of Cookies = R • t

Example 2:

Rate of motion (v) = 20 MPH
time (t) = 3 hours

Intuition or a quick Google search will reveal a formula (the distance formula) that related velocity and time of motion.

d = vt

From time to time, it is necessary to rearrange an equation so that it yields the answer you are trying to find. For example, if you trying to find time in Example 2 above, you will need to isolate the t variable. MANY TIMES it is easier to do the algebra BEFORE you plug in the numbers and units!

d = vt               (To find t divide both sides by v.) 
d/v = vt/v           (The v on the right side cancels.)
d/v = t
Once you have an equation in the form you need, you are ready for the next and final step.

The third step is to plug in what was given and solve. Assuming the second step was completed, the following solutions would emerge:

Example 1:
Cookies = R•t
Cookies = 12 Cookie/20 min • 80 min
Cookies = 960 Cookie•min / 20 min
Cookies = 48 Cookie 

Example 2:
d = vt
=  20 mi/hr * 3hr
d = 60 (mi•hr)/hr
d = 60 mi

For additional examples and a video explanation, check this out:

Scan for Video

Scan for Video

Example 3 (All together)

A car ball rolls at a constant rate of 20 m/s. How far will it roll in 8 seconds?

Using df as final distance rolled, v as the velocity, and t as time… 
Find df where
v = 20 m/s
t = 8 s
df = vt
df = (20 m/s) (8 s)
df = 160 m


There are three steps to solving problems.

1: Write down what is asked for.
2: Write down what is given and find a relevant equation.
2b: Rearrange the equation so that it yields the answer you want.
3. Plug in and solve.

The same thing expressed as five steps:

1 Write down what is being asked for.
2. Write down what is given.
3. Identify a relevant equation.
4. Plug in.
5. Solve.