Comparing the size and scale of particles

To find out how much bigger one object is than another, divide the larger value by the smaller.

Example:

Two cakes, one with a 40 cm diameter, one with a 20 cm diameter.

Larger value ÷ smaller value

= 40 ÷ 20

= 2

Comparing sizes using order of magnitude

If one number is 10 times bigger, then the sizes differ by an order of magnitude.

Example

The diameter of a hydrogen atom is 2.50 × 10-11 m and the diameter of a gold atom is 1.44 × 10-10 m.

Compare the size of a gold atom with a hydrogen atom. Do their sizes differ by an order of magnitude?

\frac{larger~value}{smaller~value} = \frac{1.44 \times 10^{-10}}{2.50 \times 10^{-11}} = 5.76

Therefore a gold atom is 5.76 times larger than a hydrogen atom. This is less than 10, so the size of a gold atom is not an order of magnitude different from the size of a hydrogen atom.

Comparing the size and scale of atoms to the real world

Some objects in the everyday world are very large. It is easier to write their size in standard form too. For example, the diameter of the Earth is about 13,000,000 m. This is 1.3 × 107 m in standard form. To compare the size of atoms to objects in the everyday world, follow the same method of dividing the larger value by the smaller.

Example

The diameter of a nucleus is about 2 × 10-15 m and the diameter of an atom is 1 × 10-10 m. What size would the atom be in a model where the Earth represented the nucleus? The diameter of the Earth is 1.3 × 107 m.

\frac{larger~value}{smaller~value} = \frac{1 \times 10^{-10}}{2 \times 10^{-15}} = 5 \times 10^4

Therefore the atom is 5 × 104 larger than the nucleus. The model of the atom must be 5 × 104 times larger than this.

diameter of the model atom

= (diameter of the Earth) × 5 × 104

= 6.5 × 1011 m

Question

If the Earth represented an atom, what size would the nucleus be? Assume that the diameter of an atom is 5 × 104 greater than the diameter of the nucleus.

diameter of model nucleus = \frac{diameter~of~Earth}{5 \times 10^4}

\frac{1.3 \times 10^7}{5 \times 10^4}

= 260 m