Particle size and scale
To find out how much bigger one object is than another, divide the larger value by the smaller.
Example:
Larger value Ă· smaller value
= 40 Ă· 20
= 2
Comparing sizes using order of magnitude
If one number is 10 times bigger than another number, their sizes differ by one order of magnitude. If a number is 100 times bigger than another number, their sizes differ by two An order of magnitude estimate approximates a number to the nearest power of ten..
Example
The smallest part of an element that can exist. are very small, approximately 1 x 10 -10. metres in diameter. This means that you need to line up 10 million atoms side by side to make a line which is 1 millimetre long.
Molecules are made from between 2 and several hundred atoms, so they are larger than the atoms which they are made from. However, molecules are still far too small to be seen with the naked eye.
The diameter of the nucleus of an atom is tiny in comparison with the diameter of the whole atom. Let us assume that a specific atom has a diameter of 1 x 10-10 metres and that its nucleus has a diameter of 1 x10-14 metres.
Compare the size of the nucleus with the size of the atom.
\(\frac{larger~value}{smaller~value} = \frac{1 \times 10^{-10}}{1 \times 10^{-14}} = 10,000\)
So the atom is 10,000 times larger than the nucleus. Another way of describing this fact is to say that the nucleus is 1/10,000 of the size of the atom.
Expressing this in orders of magnitude, we say that the diameter of the atom is four orders of magnitude greater than the diameter of the nucleus. This is because 10,000 is equal to 104.
Comparing the size and scale of atoms to the real world
Because atoms are so small, it can be difficult to understand their scale. Let’s compare an atom to a large sports stadium, which has a diameter of 300 metres.
\(\frac{300}{10,000} = 0.03 metres\)
To covert this into centimetres, multiply by 100.
0.03 x 100 = 3 centimetres.
This means that if we imagine an atom as large as a big sports stadium, the nucleus would be approximately the same size as a large marble.
Example
The diameter of a The central part of an atom. It contains protons and neutrons, and has most of the mass of the atom. The plural of nucleus is nuclei. is about 2 Ă— 10-15 m and the diameter of an atom is 1 Ă— 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 Ă— 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 Ă— 104 larger than the nucleus. The model of the atom must be 5 Ă— 104 times larger than this.
diameter of the model atom
= (diameter of the Earth) Ă— 5 Ă— 104
= 6.5 Ă— 1011 m
Question
If the Earth represented an atom, what size would the nucleus be? Assume that the diameter of an atom is 5 Ă— 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