58 3. LOOKING INWARD
3.3 THE MICROSCOPIC
An ordinary microscope is an arrangement of lenses that allows one to directly see a magnified
view of tiny objects. No matter how perfect the optics, there is a limit that cannot be surpassed;
one cannot use an ordinary microscope to see anything smaller than the wavelength of light
itself. For humans, this wavelength is roughly 5 ˆ 10
´7
m, just a bit smaller than the smallest
bacteria. And so objects smaller than this must be “viewed” by other means.
3.4 MOLECULES, ATOMS, AND THEIR PARTS
Individual atoms are roughly 10
´10
m in size, about 4 orders of magnitude—10,000 times—
smaller than the smallest objects visible through microscopes. Atoms are made of a nucleus of
protons and neutrons, surrounded by a cloud of electrons. e electrons (with a negative electric
charge) have very little of the overall mass, but they take up nearly all of the space of an atom. And
so it is the electrons that give the atom its size.
e nucleus of an atom, on the other hand, made of protons and neutrons, makes up
most of the atom’s mass but takes up very little of the space. A typical atomic nucleus is only
10
´19
m across, nine powers of ten smaller than the atom itself. is is similar to the size of Earth
compared to about one fifth of the distance to the nearest star, ˛ Centauri. And so, borrowing
from our scale model of the solar system, the nucleus of an atom is like a grain of salt in an atom
that is nearly 250 km across.
Molecules are arrangements of atoms bound to each other by electrical forces. A water
molecule, made from two atoms of hydrogen and one of oxygen, is a familiar example. It is not
much larger than a single atom of oxygen, but molecules exist that are made of many thousands
of atoms. e large rod-shaped protein molecule
fibrogen
, for example, is
50 nm
(
5
ˆ
10
´8
m
)
long [Erickson, 2009]. is is over two orders of magnitude larger than a single atom, but still
far too small to see with a microscope.
3.5 THE PLANCK LENGTH
ere is a smallest size where we know that we don’t know what is going on; the laws of physics
as presently understood simply do not hold at this scale. It can be calculated from simple as-
sumptions, combining the known physical constants in such a way that they make a length.
us, our constants that describe the speed of light (c), the strength of gravitation (G), and the
fundamental quantum of physics, Planck’s constant (h) form a length, l
P
, when combined as
follows [Ryden, 2017, Chap. 1]:
l
P
D
c
Gh
c
3
: (3.1)
is length is very tiny, and it is known as the Planck length, after the physicist Max
Planck. e Planck length is about 1:6 ˆ 10
´35
m, and at lengths smaller than that, our current
understanding of physics breaks down [Penrose, 2004, p. 872].
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