Ratio of an atom

LI: Understand ratio

If the proton nucleus of a hydrogen atom were the size of a golf ball, the electron would be orbiting 1.4 km away!  That's why we say atoms are mostly empty space!

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?

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 × 10^7 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 × 10-1^5 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 × 10^7 m.

Therefore the atom is 5 × 10^4 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 × 10^4

= 6.5 × 10^11 m

Question

If the Earth represented an atom, what size would the nucleus be? Assume that the diameter of an atom is 5 × 10^4 greater than the diameter of the nucleus.

Source: BBC Bitsize

If the nucleus was the size of a spider, the diameter of the atom would be 10 football fields.

Make your own comparison using ratio knowledge and post on classroom