Physics for scientists and engineers

Protons and neutrons

atomic number

The number of protons constituting an atom's nucleus. Often denoted Z. A given element is defined by its atomic number.

mass number

The number of protons and neutrons constituting an atom's nucleus.

Protons have a charge of 1 e by definition of e, the elementary charge.

Neutrons have a charge of 0 e.

Electrons have a charge of -1 e.

Quarks

Protons, neutrons, and a host of other exotic particles are known to be composed of six different varieties of quarks: up, down, strange, charm(ed), bottom, and top.

• Up, charm, and top each have a charge of 2/3 e.

• Down, strange, and bottom each of a charge of -1/3 e.

The quark model correctly predicts the energy of greater particles: a proton is composed of three quarks: two ups, and one down. 2 * 2/3 e + -1/3 e = 1 e — the energy of a single proton.

1.1

Suppose the three fundamental standards of the metric system were length, density, and time rather than length, mass, and time. The standard of density in this system is to be defined as that of water. What considerations about water would you need to address to make sure the standard of density is as accurate as possible?

What variables, if any, influence the density of water? Heat, pressure, etc.?

1.2

Express the following quantities using the prefixes given in Table 1.4:

1. 3 × 10⁻⁴ m

2. 5 × 10⁻⁵ s

3. 72 × 10² g

1. 30 millimetres

2. 50 micrometres

3. 0.72 kilograms

1.3

Rank the following five quantities in order from the largest to the smallest:

1. 0.032 kg

2. 15 g

3. 2.7 × 10⁵ mg

4. 4.1 × 10⁻⁸ Gg

5. 2.7 × 10⁸ μg

If two of the masses are equal, give them equal rank in your list.

Observe that you can move up and down the ladder of prefixes using the following identity:

$$a\times {10}^{3+n}\text{mg}=a\times {10}^n\text{g}$$

1. 0.032 kg = 320 g

2. 2.7 × 10⁵ mg, 2.7 × 10⁸ μg = 270 g

3. 15 g = 15 g

4. 4.1 × 10⁻⁸ Gg = 4.1 × 10⁻¹⁷ g

1.4

If an equation is dimensionally correct, does that mean that the equation must be true? If an equation is not dimensionally correct, does that mean that the equation cannot be true?

An equation being dimensionally correct does not imply that the equation is true. Example: $1\text{m}=2\text{m}$.

I do not believe I have been given enough information to formally claim whether or not the converse holds. Personally, I would take as axiom that a statement such as $1\text{m}=23\text{kg}$ is as meaningless as an ill-typed expression in Haskell. You could probably prove a contradiction, given a particular identity, such as $\text{m}=3\text{kg}$.

1.5

Answer each question yes or no. Must two quantities have the same dimensions...

1. if you are adding them?

2. If you are multiplying them?

3. If you are subtracting them?

4. If you are dividing them?

5. If you are using one quantity as an exponent in raising the other to a power?

6. If you are equating them?

1. Yes.

2. No.

3. Yes.

4. No.

5. ???

6. Yes.